Solve (5/b-3/4)div(2/3+4/9)

$$( \frac { 5 } { b } - \frac { 3 } { 4 } ) \div ( \frac { 2 } { 3 } + \frac { 4 } { 9 } )$$

Evaluate

$$-\frac{27}{40}+\frac{9}{2b}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and 4 is 4b. Multiply \frac{5}{b} times \frac{4}{4}. Multiply \frac{3}{4} times \frac{b}{b}.

$$\frac{\frac{5\times 4}{4b}-\frac{3b}{4b}}{\frac{2}{3}+\frac{4}{9}}$$

Since \frac{5\times 4}{4b} and \frac{3b}{4b} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5\times 4-3b}{4b}}{\frac{2}{3}+\frac{4}{9}}$$

Do the multiplications in 5\times 4-3b.

$$\frac{\frac{20-3b}{4b}}{\frac{2}{3}+\frac{4}{9}}$$

Least common multiple of 3 and 9 is 9. Convert \frac{2}{3} and \frac{4}{9} to fractions with denominator 9.

$$\frac{\frac{20-3b}{4b}}{\frac{6}{9}+\frac{4}{9}}$$

Since \frac{6}{9} and \frac{4}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{20-3b}{4b}}{\frac{6+4}{9}}$$

Add 6 and 4 to get 10.

$$\frac{\frac{20-3b}{4b}}{\frac{10}{9}}$$

Divide \frac{20-3b}{4b} by \frac{10}{9} by multiplying \frac{20-3b}{4b} by the reciprocal of \frac{10}{9}.

$$\frac{\left(20-3b\right)\times 9}{4b\times 10}$$

Multiply 4 and 10 to get 40.

$$\frac{\left(20-3b\right)\times 9}{40b}$$

Use the distributive property to multiply 20-3b by 9.

$$\frac{180-27b}{40b}$$

Expand

$$-\frac{27}{40}+\frac{9}{2b}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b and 4 is 4b. Multiply \frac{5}{b} times \frac{4}{4}. Multiply \frac{3}{4} times \frac{b}{b}.

$$\frac{\frac{5\times 4}{4b}-\frac{3b}{4b}}{\frac{2}{3}+\frac{4}{9}}$$

Since \frac{5\times 4}{4b} and \frac{3b}{4b} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5\times 4-3b}{4b}}{\frac{2}{3}+\frac{4}{9}}$$

Do the multiplications in 5\times 4-3b.

$$\frac{\frac{20-3b}{4b}}{\frac{2}{3}+\frac{4}{9}}$$

Least common multiple of 3 and 9 is 9. Convert \frac{2}{3} and \frac{4}{9} to fractions with denominator 9.

$$\frac{\frac{20-3b}{4b}}{\frac{6}{9}+\frac{4}{9}}$$

Since \frac{6}{9} and \frac{4}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{20-3b}{4b}}{\frac{6+4}{9}}$$

Add 6 and 4 to get 10.

$$\frac{\frac{20-3b}{4b}}{\frac{10}{9}}$$

Divide \frac{20-3b}{4b} by \frac{10}{9} by multiplying \frac{20-3b}{4b} by the reciprocal of \frac{10}{9}.

$$\frac{\left(20-3b\right)\times 9}{4b\times 10}$$

Multiply 4 and 10 to get 40.

$$\frac{\left(20-3b\right)\times 9}{40b}$$

Use the distributive property to multiply 20-3b by 9.

$$\frac{180-27b}{40b}$$