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Adding & Subtracting Rational Expressions — Easy Worksheet 2
Grade 11 · Whoobee Name: ____________________ Date: __________
Add or subtract. Type a fraction answer with parentheses, like (2x + 3)/(x - 1). When a problem asks only for the numerator, write it in standard form, like 5x - 4.
How to solve
With the same denominator, add or subtract the numerators and keep the denominator (when subtracting, change every sign of the second numerator). With different denominators, factor them and build the least common denominator (LCD): each different factor once, with its highest power. Multiply the top and bottom of each fraction by the factors its denominator is missing, then combine the numerators over the LCD, e.g. 2x + 1 + 3x - 2 = (2(x - 2) + 3(x + 1)) / ((x + 1)(x - 2)), whose numerator is 5x - 1. Finally cancel any factor the numerator and denominator share.
Example
Subtract: 8x - 1 - 2x - 1
Answer: 6x - 1
Not quite. The answer is
💡 The denominators are the same, so combine the numerators: (5x - 2) + (3x + 3) = 5x - 2 + 3x + 3 = 8x + 1. Keep the denominator. The answer is 8x + 1x - 4.
✓ Correct!
Not quite. The answer is
💡 The denominators are the same, so combine the numerators: (5x - 2) + (3x + 3) = 5x - 2 + 3x + 3 = 8x + 1. Keep the denominator. The answer is 8x + 1x - 4.
💡 How to solve: Adding & Subtracting Rational Expressions
With the same denominator, add or subtract the numerators and keep the denominator (when subtracting, change every sign of the second numerator). With different denominators, factor them and build the least common denominator (LCD): each different factor once, with its highest power. Multiply the top and bottom of each fraction by the factors its denominator is missing, then combine the numerators over the LCD, e.g. 2x + 1 + 3x - 2 = (2(x - 2) + 3(x + 1)) / ((x + 1)(x - 2)), whose numerator is 5x - 1. Finally cancel any factor the numerator and denominator share.
Try a similar one
Add: x + 2x - 9 + 5x + 1x - 9
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 For the numbers, the least common multiple of 9 and 7 is 63. For the variable, take the highest power of x, which is x². The LCD is 63x².
✓ Correct!
Not quite. The answer is
💡 For the numbers, the least common multiple of 9 and 7 is 63. For the variable, take the highest power of x, which is x². The LCD is 63x².
💡 How to solve: Adding & Subtracting Rational Expressions
With the same denominator, add or subtract the numerators and keep the denominator (when subtracting, change every sign of the second numerator). With different denominators, factor them and build the least common denominator (LCD): each different factor once, with its highest power. Multiply the top and bottom of each fraction by the factors its denominator is missing, then combine the numerators over the LCD, e.g. 2x + 1 + 3x - 2 = (2(x - 2) + 3(x + 1)) / ((x + 1)(x - 2)), whose numerator is 5x - 1. Finally cancel any factor the numerator and denominator share.
Try a similar one
Subtract: 2x + 1x + 8 - 3x + 3x + 8
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The LCD is (x + 1)(x + 7). Multiply the top and bottom of the first fraction by (x + 7) and of the second by (x + 1). The numerator is 5(x + 7) - 3(x + 1) = (5x + 35) - (3x + 3) = 2x + 32.
✓ Correct!
Not quite. The answer is
💡 The LCD is (x + 1)(x + 7). Multiply the top and bottom of the first fraction by (x + 7) and of the second by (x + 1). The numerator is 5(x + 7) - 3(x + 1) = (5x + 35) - (3x + 3) = 2x + 32.
💡 How to solve: Adding & Subtracting Rational Expressions
With the same denominator, add or subtract the numerators and keep the denominator (when subtracting, change every sign of the second numerator). With different denominators, factor them and build the least common denominator (LCD): each different factor once, with its highest power. Multiply the top and bottom of each fraction by the factors its denominator is missing, then combine the numerators over the LCD, e.g. 2x + 1 + 3x - 2 = (2(x - 2) + 3(x + 1)) / ((x + 1)(x - 2)), whose numerator is 5x - 1. Finally cancel any factor the numerator and denominator share.
Try a similar one
Subtract: 3x - 3x - 5 - 3x + 1x - 5
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The LCD is x². Multiply the top and bottom of 7x by x to get 7xx². Now 7x − 4 goes over x², so the numerator is 7x - 4.
✓ Correct!
Not quite. The answer is
💡 The LCD is x². Multiply the top and bottom of 7x by x to get 7xx². Now 7x − 4 goes over x², so the numerator is 7x - 4.
💡 How to solve: Adding & Subtracting Rational Expressions
With the same denominator, add or subtract the numerators and keep the denominator (when subtracting, change every sign of the second numerator). With different denominators, factor them and build the least common denominator (LCD): each different factor once, with its highest power. Multiply the top and bottom of each fraction by the factors its denominator is missing, then combine the numerators over the LCD, e.g. 2x + 1 + 3x - 2 = (2(x - 2) + 3(x + 1)) / ((x + 1)(x - 2)), whose numerator is 5x - 1. Finally cancel any factor the numerator and denominator share.
Try a similar one
Add: 4x + 4x + 1 + 2x + 4x + 1
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The denominators are the same, so combine the numerators: (x + 5) + (5x - 2) = x + 5 + 5x - 2 = 6x + 3. Keep the denominator. The answer is 6x + 3x - 2.
✓ Correct!
Not quite. The answer is
💡 The denominators are the same, so combine the numerators: (x + 5) + (5x - 2) = x + 5 + 5x - 2 = 6x + 3. Keep the denominator. The answer is 6x + 3x - 2.
💡 How to solve: Adding & Subtracting Rational Expressions
With the same denominator, add or subtract the numerators and keep the denominator (when subtracting, change every sign of the second numerator). With different denominators, factor them and build the least common denominator (LCD): each different factor once, with its highest power. Multiply the top and bottom of each fraction by the factors its denominator is missing, then combine the numerators over the LCD, e.g. 2x + 1 + 3x - 2 = (2(x - 2) + 3(x + 1)) / ((x + 1)(x - 2)), whose numerator is 5x - 1. Finally cancel any factor the numerator and denominator share.
Try a similar one
Subtract: x - 1x + 1 - x - 4x + 1
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The LCD is (x - 4)(x - 8). Multiply the top and bottom of the first fraction by (x - 8) and of the second by (x - 4). The numerator is 5(x - 8) - 2(x - 4) = (5x - 40) - (2x - 8) = 3x - 32.
✓ Correct!
Not quite. The answer is
💡 The LCD is (x - 4)(x - 8). Multiply the top and bottom of the first fraction by (x - 8) and of the second by (x - 4). The numerator is 5(x - 8) - 2(x - 4) = (5x - 40) - (2x - 8) = 3x - 32.
💡 How to solve: Adding & Subtracting Rational Expressions
With the same denominator, add or subtract the numerators and keep the denominator (when subtracting, change every sign of the second numerator). With different denominators, factor them and build the least common denominator (LCD): each different factor once, with its highest power. Multiply the top and bottom of each fraction by the factors its denominator is missing, then combine the numerators over the LCD, e.g. 2x + 1 + 3x - 2 = (2(x - 2) + 3(x + 1)) / ((x + 1)(x - 2)), whose numerator is 5x - 1. Finally cancel any factor the numerator and denominator share.
Try a similar one
Add: 5x - 4x + 3 + x + 1x + 3
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The denominators are the same, so combine the numerators, changing every sign of the second one: (x - 2) - (4x + 1) = x - 2 - 4x - 1 = -3x - 3. Keep the denominator. The answer is -3x - 3x - 2.
✓ Correct!
Not quite. The answer is
💡 The denominators are the same, so combine the numerators, changing every sign of the second one: (x - 2) - (4x + 1) = x - 2 - 4x - 1 = -3x - 3. Keep the denominator. The answer is -3x - 3x - 2.
💡 How to solve: Adding & Subtracting Rational Expressions
With the same denominator, add or subtract the numerators and keep the denominator (when subtracting, change every sign of the second numerator). With different denominators, factor them and build the least common denominator (LCD): each different factor once, with its highest power. Multiply the top and bottom of each fraction by the factors its denominator is missing, then combine the numerators over the LCD, e.g. 2x + 1 + 3x - 2 = (2(x - 2) + 3(x + 1)) / ((x + 1)(x - 2)), whose numerator is 5x - 1. Finally cancel any factor the numerator and denominator share.
Try a similar one
Subtract: 6x + 1x - 4 - 2x - 3x - 4
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The denominators (x + 8) and (x + 6) share no factor, so the LCD is their product: (x + 8)(x + 6).
✓ Correct!
Not quite. The answer is
💡 The denominators (x + 8) and (x + 6) share no factor, so the LCD is their product: (x + 8)(x + 6).
💡 How to solve: Adding & Subtracting Rational Expressions
With the same denominator, add or subtract the numerators and keep the denominator (when subtracting, change every sign of the second numerator). With different denominators, factor them and build the least common denominator (LCD): each different factor once, with its highest power. Multiply the top and bottom of each fraction by the factors its denominator is missing, then combine the numerators over the LCD, e.g. 2x + 1 + 3x - 2 = (2(x - 2) + 3(x + 1)) / ((x + 1)(x - 2)), whose numerator is 5x - 1. Finally cancel any factor the numerator and denominator share.
Try a similar one
Add: 2x + 3x - 9 + x + 2x - 9
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Adding & Subtracting Rational Expressions — Easy Worksheet 2
Add or subtract. Type a fraction answer with parentheses, like (2x + 3)/(x - 1). When a problem asks only for the numerator, write it in standard form, like 5x - 4.