Solve a+b-1/a+b

$$a + b - \frac { 1 } { a + b }$$

Evaluate

$$a+b-\frac{1}{a+b}$$

Short Solution Steps

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

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

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

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

Do the multiplications in \left(a+b\right)\left(a+b\right)-1.

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

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

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

Differentiate w.r.t. a

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