Solve 2p+q/p-2q+p+3q/2q-p

$$\frac { 2 p + q } { p - 2 q } + \frac { p + 3 q } { 2 q - p }$$

Evaluate

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Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of p-2q and 2q-p is -p+2q. Multiply \frac{2p+q}{p-2q} times \frac{-1}{-1}.

$$\frac{-\left(2p+q\right)}{-p+2q}+\frac{p+3q}{-p+2q}$$

Since \frac{-\left(2p+q\right)}{-p+2q} and \frac{p+3q}{-p+2q} have the same denominator, add them by adding their numerators.

$$\frac{-\left(2p+q\right)+p+3q}{-p+2q}$$

Do the multiplications in -\left(2p+q\right)+p+3q.

$$\frac{-2p-q+p+3q}{-p+2q}$$

Combine like terms in -2p-q+p+3q.

$$\frac{-p+2q}{-p+2q}$$

Cancel out -p+2q in both numerator and denominator.

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Factor

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