Solve x/frac{x{a}+x/b}

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and b is ab. Multiply \frac{x}{a} times \frac{b}{b}. Multiply \frac{x}{b} times \frac{a}{a}.

$$\frac{x}{\frac{xb}{ab}+\frac{xa}{ab}}$$

Since \frac{xb}{ab} and \frac{xa}{ab} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{xb+xa}{ab}}$$

Divide x by \frac{xb+xa}{ab} by multiplying x by the reciprocal of \frac{xb+xa}{ab}.

$$\frac{xab}{xb+xa}$$

Factor the expressions that are not already factored.

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

Cancel out x in both numerator and denominator.

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

Differentiate w.r.t. a

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