Solve w(1/2+3/4)-(1/5+frac{3/7)}{x(frac{8}{3}-frac{5}{2})+(frac{3}{4}divfrac{1}{2})}=

$$\frac { w ( \frac { 1 } { 2 } + \frac { 3 } { 4 } ) - ( \frac { 1 } { 5 } + \frac { 3 } { 7 } ) } { x ( \frac { 8 } { 3 } - \frac { 5 } { 2 } ) + ( \frac { 3 } { 4 } \div \frac { 1 } { 2 } ) } =$$

Evaluate

$$\frac{3\left(175w-88\right)}{70\left(x+9\right)}$$

Short Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{w\left(\frac{2}{4}+\frac{3}{4}\right)-\left(\frac{1}{5}+\frac{3}{7}\right)}{x\left(\frac{8}{3}-\frac{5}{2}\right)+\frac{\frac{3}{4}}{\frac{1}{2}}}$$

Since \frac{2}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{w\times \frac{2+3}{4}-\left(\frac{1}{5}+\frac{3}{7}\right)}{x\left(\frac{8}{3}-\frac{5}{2}\right)+\frac{\frac{3}{4}}{\frac{1}{2}}}$$

Add 2 and 3 to get 5.

$$\frac{w\times \frac{5}{4}-\left(\frac{1}{5}+\frac{3}{7}\right)}{x\left(\frac{8}{3}-\frac{5}{2}\right)+\frac{\frac{3}{4}}{\frac{1}{2}}}$$

Least common multiple of 5 and 7 is 35. Convert \frac{1}{5} and \frac{3}{7} to fractions with denominator 35.

$$\frac{w\times \frac{5}{4}-\left(\frac{7}{35}+\frac{15}{35}\right)}{x\left(\frac{8}{3}-\frac{5}{2}\right)+\frac{\frac{3}{4}}{\frac{1}{2}}}$$

Since \frac{7}{35} and \frac{15}{35} have the same denominator, add them by adding their numerators.

$$\frac{w\times \frac{5}{4}-\frac{7+15}{35}}{x\left(\frac{8}{3}-\frac{5}{2}\right)+\frac{\frac{3}{4}}{\frac{1}{2}}}$$

Add 7 and 15 to get 22.

$$\frac{w\times \frac{5}{4}-\frac{22}{35}}{x\left(\frac{8}{3}-\frac{5}{2}\right)+\frac{\frac{3}{4}}{\frac{1}{2}}}$$

Least common multiple of 3 and 2 is 6. Convert \frac{8}{3} and \frac{5}{2} to fractions with denominator 6.

$$\frac{w\times \frac{5}{4}-\frac{22}{35}}{x\left(\frac{16}{6}-\frac{15}{6}\right)+\frac{\frac{3}{4}}{\frac{1}{2}}}$$

Since \frac{16}{6} and \frac{15}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{w\times \frac{5}{4}-\frac{22}{35}}{x\times \frac{16-15}{6}+\frac{\frac{3}{4}}{\frac{1}{2}}}$$

Subtract 15 from 16 to get 1.

$$\frac{w\times \frac{5}{4}-\frac{22}{35}}{x\times \frac{1}{6}+\frac{\frac{3}{4}}{\frac{1}{2}}}$$

Divide \frac{3}{4} by \frac{1}{2} by multiplying \frac{3}{4} by the reciprocal of \frac{1}{2}.

$$\frac{w\times \frac{5}{4}-\frac{22}{35}}{x\times \frac{1}{6}+\frac{3}{4}\times 2}$$

Express \frac{3}{4}\times 2 as a single fraction.

$$\frac{w\times \frac{5}{4}-\frac{22}{35}}{x\times \frac{1}{6}+\frac{3\times 2}{4}}$$

Multiply 3 and 2 to get 6.

$$\frac{w\times \frac{5}{4}-\frac{22}{35}}{x\times \frac{1}{6}+\frac{6}{4}}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{w\times \frac{5}{4}-\frac{22}{35}}{x\times \frac{1}{6}+\frac{3}{2}}$$

Expand

$$\frac{3\left(175w-88\right)}{70\left(x+9\right)}$$

Short Solution Steps

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{w\left(\frac{2}{4}+\frac{3}{4}\right)-\left(\frac{1}{5}+\frac{3}{7}\right)}{x\left(\frac{8}{3}-\frac{5}{2}\right)+\frac{\frac{3}{4}}{\frac{1}{2}}}$$

Since \frac{2}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{w\times \frac{2+3}{4}-\left(\frac{1}{5}+\frac{3}{7}\right)}{x\left(\frac{8}{3}-\frac{5}{2}\right)+\frac{\frac{3}{4}}{\frac{1}{2}}}$$

Add 2 and 3 to get 5.

$$\frac{w\times \frac{5}{4}-\left(\frac{1}{5}+\frac{3}{7}\right)}{x\left(\frac{8}{3}-\frac{5}{2}\right)+\frac{\frac{3}{4}}{\frac{1}{2}}}$$

Least common multiple of 5 and 7 is 35. Convert \frac{1}{5} and \frac{3}{7} to fractions with denominator 35.

$$\frac{w\times \frac{5}{4}-\left(\frac{7}{35}+\frac{15}{35}\right)}{x\left(\frac{8}{3}-\frac{5}{2}\right)+\frac{\frac{3}{4}}{\frac{1}{2}}}$$

Since \frac{7}{35} and \frac{15}{35} have the same denominator, add them by adding their numerators.

$$\frac{w\times \frac{5}{4}-\frac{7+15}{35}}{x\left(\frac{8}{3}-\frac{5}{2}\right)+\frac{\frac{3}{4}}{\frac{1}{2}}}$$

Add 7 and 15 to get 22.

$$\frac{w\times \frac{5}{4}-\frac{22}{35}}{x\left(\frac{8}{3}-\frac{5}{2}\right)+\frac{\frac{3}{4}}{\frac{1}{2}}}$$

Least common multiple of 3 and 2 is 6. Convert \frac{8}{3} and \frac{5}{2} to fractions with denominator 6.

$$\frac{w\times \frac{5}{4}-\frac{22}{35}}{x\left(\frac{16}{6}-\frac{15}{6}\right)+\frac{\frac{3}{4}}{\frac{1}{2}}}$$

Since \frac{16}{6} and \frac{15}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{w\times \frac{5}{4}-\frac{22}{35}}{x\times \frac{16-15}{6}+\frac{\frac{3}{4}}{\frac{1}{2}}}$$

Subtract 15 from 16 to get 1.

$$\frac{w\times \frac{5}{4}-\frac{22}{35}}{x\times \frac{1}{6}+\frac{\frac{3}{4}}{\frac{1}{2}}}$$

Divide \frac{3}{4} by \frac{1}{2} by multiplying \frac{3}{4} by the reciprocal of \frac{1}{2}.

$$\frac{w\times \frac{5}{4}-\frac{22}{35}}{x\times \frac{1}{6}+\frac{3}{4}\times 2}$$

Express \frac{3}{4}\times 2 as a single fraction.

$$\frac{w\times \frac{5}{4}-\frac{22}{35}}{x\times \frac{1}{6}+\frac{3\times 2}{4}}$$

Multiply 3 and 2 to get 6.

$$\frac{w\times \frac{5}{4}-\frac{22}{35}}{x\times \frac{1}{6}+\frac{6}{4}}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{w\times \frac{5}{4}-\frac{22}{35}}{x\times \frac{1}{6}+\frac{3}{2}}$$