Solve 2/b+5/a/frac{3{a}-8/b}

$$\frac { \frac { 2 } { b } + \frac { 5 } { a } } { \frac { 3 } { a } - \frac { 8 } { b } }$$

Evaluate

$$\frac{2a+5b}{3b-8a}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and a is ab. Multiply \frac{2}{b} times \frac{a}{a}. Multiply \frac{5}{a} times \frac{b}{b}.

$$\frac{\frac{2a}{ab}+\frac{5b}{ab}}{\frac{3}{a}-\frac{8}{b}}$$

Since \frac{2a}{ab} and \frac{5b}{ab} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2a+5b}{ab}}{\frac{3}{a}-\frac{8}{b}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and b is ab. Multiply \frac{3}{a} times \frac{b}{b}. Multiply \frac{8}{b} times \frac{a}{a}.

$$\frac{\frac{2a+5b}{ab}}{\frac{3b}{ab}-\frac{8a}{ab}}$$

Since \frac{3b}{ab} and \frac{8a}{ab} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2a+5b}{ab}}{\frac{3b-8a}{ab}}$$

Divide \frac{2a+5b}{ab} by \frac{3b-8a}{ab} by multiplying \frac{2a+5b}{ab} by the reciprocal of \frac{3b-8a}{ab}.

$$\frac{\left(2a+5b\right)ab}{ab\left(3b-8a\right)}$$

Cancel out ab in both numerator and denominator.

$$\frac{2a+5b}{-8a+3b}$$

Expand

$$\frac{2a+5b}{3b-8a}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and a is ab. Multiply \frac{2}{b} times \frac{a}{a}. Multiply \frac{5}{a} times \frac{b}{b}.

$$\frac{\frac{2a}{ab}+\frac{5b}{ab}}{\frac{3}{a}-\frac{8}{b}}$$

Since \frac{2a}{ab} and \frac{5b}{ab} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2a+5b}{ab}}{\frac{3}{a}-\frac{8}{b}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and b is ab. Multiply \frac{3}{a} times \frac{b}{b}. Multiply \frac{8}{b} times \frac{a}{a}.

$$\frac{\frac{2a+5b}{ab}}{\frac{3b}{ab}-\frac{8a}{ab}}$$

Since \frac{3b}{ab} and \frac{8a}{ab} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2a+5b}{ab}}{\frac{3b-8a}{ab}}$$

Divide \frac{2a+5b}{ab} by \frac{3b-8a}{ab} by multiplying \frac{2a+5b}{ab} by the reciprocal of \frac{3b-8a}{ab}.

$$\frac{\left(2a+5b\right)ab}{ab\left(3b-8a\right)}$$

Cancel out ab in both numerator and denominator.

$$\frac{2a+5b}{-8a+3b}$$