Solve 1/1+a+1/1+b

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

Evaluate

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

Short Solution Steps

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

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

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

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

Combine like terms in b+1+a+1.

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

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

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

Differentiate w.r.t. b

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