Type a math problem

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Type a math problem

Evaluate

\frac{14-x}{\left(x-2\right)\left(x+1\right)}

$(x−2)(x+1)14−x $

Short Solution Steps

\frac{4}{x-2} - \frac{5}{x+1}

$x−24 −x+15 $

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}.

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x−2$ and $x+1$ is $(x−2)(x+1)$. Multiply $x−24 $ times $x+1x+1 $. Multiply $x+15 $ times $x−2x−2 $.

\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)}

$(x−2)(x+1)4(x+1) −(x−2)(x+1)5(x−2) $

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.

Since $(x−2)(x+1)4(x+1) $ and $(x−2)(x+1)5(x−2) $ have the same denominator, subtract them by subtracting their numerators.

\frac{4\left(x+1\right)-5\left(x-2\right)}{\left(x-2\right)\left(x+1\right)}

$(x−2)(x+1)4(x+1)−5(x−2) $

Do the multiplications in 4\left(x+1\right)-5\left(x-2\right).

Do the multiplications in $4(x+1)−5(x−2)$.

\frac{4x+4-5x+10}{\left(x-2\right)\left(x+1\right)}

$(x−2)(x+1)4x+4−5x+10 $

Combine like terms in 4x+4-5x+10.

Combine like terms in $4x+4−5x+10$.

\frac{-x+14}{\left(x-2\right)\left(x+1\right)}

$(x−2)(x+1)−x+14 $

Expand \left(x-2\right)\left(x+1\right).

Expand $(x−2)(x+1)$.

\frac{-x+14}{x^{2}-x-2}

$x_{2}−x−2−x+14 $

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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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