Solve [(1-5/6)*(5/2-1/3)*72/13]-x}:x=(1+frac{1}{4}):[(6-frac{21}{14})*frac{7}{3}]

$$[ ( 1 - \frac { 5 } { 6 } ) \cdot ( \frac { 5 } { 2 } - \frac { 1 } { 3 } ) \cdot \frac { 72 } { 13 } ] - x \} : x = ( 1 + \frac { 1 } { 4 } ) : [ ( 6 - \frac { 21 } { 14 } ) \cdot \frac { 7 } { 3 } ]$$

Evaluate

$$2-x$$

Solution Steps

Convert 1 to fraction \frac{6}{6}.

$$\left(\frac{6}{6}-\frac{5}{6}\right)\left(\frac{5}{2}-\frac{1}{3}\right)\times \frac{72}{13}-x$$

Since \frac{6}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-5}{6}\left(\frac{5}{2}-\frac{1}{3}\right)\times \frac{72}{13}-x$$

Subtract 5 from 6 to get 1.

$$\frac{1}{6}\left(\frac{5}{2}-\frac{1}{3}\right)\times \frac{72}{13}-x$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{1}{6}\left(\frac{15}{6}-\frac{2}{6}\right)\times \frac{72}{13}-x$$

Since \frac{15}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{6}\times \frac{15-2}{6}\times \frac{72}{13}-x$$

Subtract 2 from 15 to get 13.

$$\frac{1}{6}\times \frac{13}{6}\times \frac{72}{13}-x$$

Multiply \frac{1}{6} times \frac{13}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 13}{6\times 6}\times \frac{72}{13}-x$$

Do the multiplications in the fraction \frac{1\times 13}{6\times 6}.

$$\frac{13}{36}\times \frac{72}{13}-x$$

Multiply \frac{13}{36} times \frac{72}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 72}{36\times 13}-x$$

Cancel out 13 in both numerator and denominator.

$$\frac{72}{36}-x$$

Divide 72 by 36 to get 2.

$$2-x$$

Expand

$$2-x$$

Solution Steps

Convert 1 to fraction \frac{6}{6}.

$$\left(\frac{6}{6}-\frac{5}{6}\right)\left(\frac{5}{2}-\frac{1}{3}\right)\times \frac{72}{13}-x$$

Since \frac{6}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-5}{6}\left(\frac{5}{2}-\frac{1}{3}\right)\times \frac{72}{13}-x$$

Subtract 5 from 6 to get 1.

$$\frac{1}{6}\left(\frac{5}{2}-\frac{1}{3}\right)\times \frac{72}{13}-x$$

Least common multiple of 2 and 3 is 6. Convert \frac{5}{2} and \frac{1}{3} to fractions with denominator 6.

$$\frac{1}{6}\left(\frac{15}{6}-\frac{2}{6}\right)\times \frac{72}{13}-x$$

Since \frac{15}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{6}\times \frac{15-2}{6}\times \frac{72}{13}-x$$

Subtract 2 from 15 to get 13.

$$\frac{1}{6}\times \frac{13}{6}\times \frac{72}{13}-x$$

Multiply \frac{1}{6} times \frac{13}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 13}{6\times 6}\times \frac{72}{13}-x$$

Do the multiplications in the fraction \frac{1\times 13}{6\times 6}.

$$\frac{13}{36}\times \frac{72}{13}-x$$

Multiply \frac{13}{36} times \frac{72}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 72}{36\times 13}-x$$

Cancel out 13 in both numerator and denominator.

$$\frac{72}{36}-x$$

Divide 72 by 36 to get 2.

$$2-x$$