Solve a/a+1-a^2/a^2-1

$$\frac { a } { a + 1 } - \frac { a ^ { 2 } } { a ^ { 2 } - 1 }$$

Evaluate

$$-\frac{a}{a^{2}-1}$$

Short Solution Steps

Factor a^{2}-1.

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

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

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

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

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

Do the multiplications in a\left(a-1\right)-a^{2}.

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

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

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

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

$$\frac{-a}{a^{2}-1}$$

Factor

$$-\frac{a}{a^{2}-1}$$