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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

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

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

Use the distributive property to multiply a+b by a.

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

Use the distributive property to multiply b by a-b.

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

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

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

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

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

Use the distributive property to multiply a+b by a.

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

Use the distributive property to multiply b by a-b.

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