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

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a^{2}-1 times \frac{a+1}{a+1}.

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

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

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

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

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

Combine like terms in a^{3}+a^{2}-a-1-1.

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

Differentiate w.r.t. a

$$\frac{2a^{3}+4a^{2}+2a+1}{\left(a+1\right)^{2}}$$