Solve x/4-7/3+7/9

$$\frac { x } { 4 } - \frac { 7 } { 3 } + \frac { 7 } { 9 }$$

Evaluate

$$\frac{x}{4}-\frac{14}{9}$$

Short Solution Steps

Least common multiple of 3 and 9 is 9. Convert -\frac{7}{3} and \frac{7}{9} to fractions with denominator 9.

$$\frac{x}{4}-\frac{21}{9}+\frac{7}{9}$$

Since -\frac{21}{9} and \frac{7}{9} have the same denominator, add them by adding their numerators.

$$\frac{x}{4}+\frac{-21+7}{9}$$

Add -21 and 7 to get -14.

$$\frac{x}{4}-\frac{14}{9}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 9 is 36. Multiply \frac{x}{4} times \frac{9}{9}. Multiply \frac{14}{9} times \frac{4}{4}.

$$\frac{9x}{36}-\frac{14\times 4}{36}$$

Since \frac{9x}{36} and \frac{14\times 4}{36} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9x-14\times 4}{36}$$

Do the multiplications in 9x-14\times 4.

$$\frac{9x-56}{36}$$

Factor

$$\frac{9x-56}{36}$$

Solution Steps

Factor out \frac{1}{36}.

$$\frac{9x-56}{36}$$

Consider 9x-84+28. Multiply and combine like terms.

$$9x-56$$

Rewrite the complete factored expression.

$$\frac{9x-56}{36}$$