Solve 3a/a-2-5a/a+1

$$\frac { 3 a } { a - 2 } - \frac { 5 a } { a + 1 }$$

Evaluate

$$\frac{a\left(13-2a\right)}{\left(a-2\right)\left(a+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a-2 and a+1 is \left(a-2\right)\left(a+1\right). Multiply \frac{3a}{a-2} times \frac{a+1}{a+1}. Multiply \frac{5a}{a+1} times \frac{a-2}{a-2}.

$$\frac{3a\left(a+1\right)}{\left(a-2\right)\left(a+1\right)}-\frac{5a\left(a-2\right)}{\left(a-2\right)\left(a+1\right)}$$

Since \frac{3a\left(a+1\right)}{\left(a-2\right)\left(a+1\right)} and \frac{5a\left(a-2\right)}{\left(a-2\right)\left(a+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3a\left(a+1\right)-5a\left(a-2\right)}{\left(a-2\right)\left(a+1\right)}$$

Do the multiplications in 3a\left(a+1\right)-5a\left(a-2\right).

$$\frac{3a^{2}+3a-5a^{2}+10a}{\left(a-2\right)\left(a+1\right)}$$

Combine like terms in 3a^{2}+3a-5a^{2}+10a.

$$\frac{-2a^{2}+13a}{\left(a-2\right)\left(a+1\right)}$$

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

$$\frac{-2a^{2}+13a}{a^{2}-a-2}$$

Factor

$$\frac{a\left(13-2a\right)}{\left(a-2\right)\left(a+1\right)}$$