Solve 1/a+3/2b/frac{1{a}-3/5b}

$$\frac { \frac { 1 } { a } + \frac { 3 } { 2 b } } { \frac { 1 } { a } - \frac { 3 } { 5 b } }$$

Evaluate

$$\frac{5\left(3a+2b\right)}{2\left(5b-3a\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and 2b is 2ab. Multiply \frac{1}{a} times \frac{2b}{2b}. Multiply \frac{3}{2b} times \frac{a}{a}.

$$\frac{\frac{2b}{2ab}+\frac{3a}{2ab}}{\frac{1}{a}-\frac{3}{5b}}$$

Since \frac{2b}{2ab} and \frac{3a}{2ab} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2b+3a}{2ab}}{\frac{1}{a}-\frac{3}{5b}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and 5b is 5ab. Multiply \frac{1}{a} times \frac{5b}{5b}. Multiply \frac{3}{5b} times \frac{a}{a}.

$$\frac{\frac{2b+3a}{2ab}}{\frac{5b}{5ab}-\frac{3a}{5ab}}$$

Since \frac{5b}{5ab} and \frac{3a}{5ab} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2b+3a}{2ab}}{\frac{5b-3a}{5ab}}$$

Divide \frac{2b+3a}{2ab} by \frac{5b-3a}{5ab} by multiplying \frac{2b+3a}{2ab} by the reciprocal of \frac{5b-3a}{5ab}.

$$\frac{\left(2b+3a\right)\times 5ab}{2ab\left(5b-3a\right)}$$

Cancel out ab in both numerator and denominator.

$$\frac{5\left(3a+2b\right)}{2\left(-3a+5b\right)}$$

Use the distributive property to multiply 5 by 3a+2b.

$$\frac{15a+10b}{2\left(-3a+5b\right)}$$

Use the distributive property to multiply 2 by -3a+5b.

$$\frac{15a+10b}{-6a+10b}$$

Expand

$$\frac{5\left(3a+2b\right)}{2\left(5b-3a\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and 2b is 2ab. Multiply \frac{1}{a} times \frac{2b}{2b}. Multiply \frac{3}{2b} times \frac{a}{a}.

$$\frac{\frac{2b}{2ab}+\frac{3a}{2ab}}{\frac{1}{a}-\frac{3}{5b}}$$

Since \frac{2b}{2ab} and \frac{3a}{2ab} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2b+3a}{2ab}}{\frac{1}{a}-\frac{3}{5b}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and 5b is 5ab. Multiply \frac{1}{a} times \frac{5b}{5b}. Multiply \frac{3}{5b} times \frac{a}{a}.

$$\frac{\frac{2b+3a}{2ab}}{\frac{5b}{5ab}-\frac{3a}{5ab}}$$

Since \frac{5b}{5ab} and \frac{3a}{5ab} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2b+3a}{2ab}}{\frac{5b-3a}{5ab}}$$

Divide \frac{2b+3a}{2ab} by \frac{5b-3a}{5ab} by multiplying \frac{2b+3a}{2ab} by the reciprocal of \frac{5b-3a}{5ab}.

$$\frac{\left(2b+3a\right)\times 5ab}{2ab\left(5b-3a\right)}$$

Cancel out ab in both numerator and denominator.

$$\frac{5\left(3a+2b\right)}{2\left(-3a+5b\right)}$$

Use the distributive property to multiply 5 by 3a+2b.

$$\frac{15a+10b}{2\left(-3a+5b\right)}$$

Use the distributive property to multiply 2 by -3a+5b.

$$\frac{15a+10b}{-6a+10b}$$