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To add or subtract expressions, expand them to make their denominators the same. Least common multiple of and is . Multiply times . Multiply times .
Since and have the same denominator, subtract them by subtracting their numerators.
Do the multiplications in .
Combine like terms in .
Expand .
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\frac{4\left(x+1\right)}{\left(x-2\right)\left(x+1\right)}-\frac{5\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and x+1 is \left(x-2\right)\left(x+1\right). Multiply \frac{4}{x-2} times \frac{x+1}{x+1}. Multiply \frac{5}{x+1} times \frac{x-2}{x-2}.
\frac{4\left(x+1\right)-5\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}
Since \frac{4\left(x+1\right)}{\left(x-2\right)\left(x+1\right)} and \frac{5\left(x-2\right)}{\left(x-2\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{4x+4-5x+10}{\left(x-2\right)\left(x+1\right)}
Do the multiplications in 4\left(x+1\right)-5\left(x-2\right).
\frac{-x+14}{\left(x-2\right)\left(x+1\right)}
Combine like terms in 4x+4-5x+10.
\frac{-x+14}{x^{2}-x-2}
Expand \left(x-2\right)\left(x+1\right).
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