Solve (1-b/a+b)diva/a^2-b^2

$$( 1 - \frac { b } { a + b } ) \div \frac { a } { a ^ { 2 } - b ^ { 2 } }$$

Evaluate

$$a-b$$

Short Solution Steps

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

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

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

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

Combine like terms in a+b-b.

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

Divide \frac{a}{a+b} by \frac{a}{a^{2}-b^{2}} by multiplying \frac{a}{a+b} by the reciprocal of \frac{a}{a^{2}-b^{2}}.

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

Cancel out a in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out a+b in both numerator and denominator.

$$a-b$$

Expand

$$a-b$$

Short Solution Steps

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

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

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

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

Combine like terms in a+b-b.

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

Divide \frac{a}{a+b} by \frac{a}{a^{2}-b^{2}} by multiplying \frac{a}{a+b} by the reciprocal of \frac{a}{a^{2}-b^{2}}.

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

Cancel out a in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out a+b in both numerator and denominator.

$$a-b$$