Solve (1+a/b):(1-a/b)

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

Cancel out b in both numerator and denominator.

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

Expand

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

Cancel out b in both numerator and denominator.

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