Solve 1-a/b/1+frac{a{b}}

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{b}{b}.

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

Since \frac{b}{b} and \frac{a}{b} have the same denominator, add them by adding their numerators.

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

Divide \frac{a}{b} by \frac{b+a}{b} by multiplying \frac{a}{b} by the reciprocal of \frac{b+a}{b}.

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

Cancel out b in both numerator and denominator.

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

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

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

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

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

Combine like terms in a+b-a.

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

Differentiate w.r.t. b

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