Solve a/a+5-a^2/a^2-25

$$\frac { a } { a + 5 } - \frac { a ^ { 2 } } { a ^ { 2 } - 25 }$$

Evaluate

$$-\frac{5a}{a^{2}-25}$$

Short Solution Steps

Factor a^{2}-25.

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

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

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

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

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

Do the multiplications in a\left(a-5\right)-a^{2}.

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

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

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

Expand \left(a-5\right)\left(a+5\right).

$$\frac{-5a}{a^{2}-25}$$

Factor

$$-\frac{5a}{a^{2}-25}$$