Solve 14/32-12-2+2/2-4=3/8-22-5/6

$$\frac { 14 } { 32 - 12 } - \frac { 2 + 2 } { 2 - 4 } = \frac { 3 } { 8 - 22 } - \frac { 5 } { 6 }$$

Verify

Solution Steps

Subtract 12 from 32 to get 20.

$$\frac{14}{20}-\frac{2+2}{2-4}=\frac{3}{8-22}-\frac{5}{6}$$

Reduce the fraction \frac{14}{20} to lowest terms by extracting and canceling out 2.

$$\frac{7}{10}-\frac{2+2}{2-4}=\frac{3}{8-22}-\frac{5}{6}$$

Add 2 and 2 to get 4.

$$\frac{7}{10}-\frac{4}{2-4}=\frac{3}{8-22}-\frac{5}{6}$$

Subtract 4 from 2 to get -2.

$$\frac{7}{10}-\frac{4}{-2}=\frac{3}{8-22}-\frac{5}{6}$$

Divide 4 by -2 to get -2.

$$\frac{7}{10}-\left(-2\right)=\frac{3}{8-22}-\frac{5}{6}$$

The opposite of -2 is 2.

$$\frac{7}{10}+2=\frac{3}{8-22}-\frac{5}{6}$$

Convert 2 to fraction \frac{20}{10}.

$$\frac{7}{10}+\frac{20}{10}=\frac{3}{8-22}-\frac{5}{6}$$

Since \frac{7}{10} and \frac{20}{10} have the same denominator, add them by adding their numerators.

$$\frac{7+20}{10}=\frac{3}{8-22}-\frac{5}{6}$$

Add 7 and 20 to get 27.

$$\frac{27}{10}=\frac{3}{8-22}-\frac{5}{6}$$

Subtract 22 from 8 to get -14.

$$\frac{27}{10}=\frac{3}{-14}-\frac{5}{6}$$

Fraction \frac{3}{-14} can be rewritten as -\frac{3}{14} by extracting the negative sign.

$$\frac{27}{10}=-\frac{3}{14}-\frac{5}{6}$$

Least common multiple of 14 and 6 is 42. Convert -\frac{3}{14} and \frac{5}{6} to fractions with denominator 42.

$$\frac{27}{10}=-\frac{9}{42}-\frac{35}{42}$$

Since -\frac{9}{42} and \frac{35}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27}{10}=\frac{-9-35}{42}$$

Subtract 35 from -9 to get -44.

$$\frac{27}{10}=\frac{-44}{42}$$

Reduce the fraction \frac{-44}{42} to lowest terms by extracting and canceling out 2.

$$\frac{27}{10}=-\frac{22}{21}$$

Least common multiple of 10 and 21 is 210. Convert \frac{27}{10} and -\frac{22}{21} to fractions with denominator 210.

$$\frac{567}{210}=-\frac{220}{210}$$

Compare \frac{567}{210} and -\frac{220}{210}.

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