Solve 7/3x+3/4+4/8/frac{5{7}-frac{8}{6}*frac{6}{3}}

$$\frac { \frac { 7 } { 3 } x + \frac { 3 } { 4 } + \frac { 4 } { 8 } } { \frac { 5 } { 7 } - \frac { 8 } { 6 } \times \frac { 6 } { 3 } }$$

Evaluate

$$-\frac{49x}{41}-\frac{105}{164}$$

Solution Steps

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{7}{3}x+\frac{3}{4}+\frac{1}{2}}{\frac{5}{7}-\frac{8}{6}\times \frac{6}{3}}$$

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

$$\frac{\frac{7}{3}x+\frac{3}{4}+\frac{2}{4}}{\frac{5}{7}-\frac{8}{6}\times \frac{6}{3}}$$

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

$$\frac{\frac{7}{3}x+\frac{3+2}{4}}{\frac{5}{7}-\frac{8}{6}\times \frac{6}{3}}$$

Add 3 and 2 to get 5.

$$\frac{\frac{7}{3}x+\frac{5}{4}}{\frac{5}{7}-\frac{8}{6}\times \frac{6}{3}}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{7}{3}x+\frac{5}{4}}{\frac{5}{7}-\frac{4}{3}\times \frac{6}{3}}$$

Divide 6 by 3 to get 2.

$$\frac{\frac{7}{3}x+\frac{5}{4}}{\frac{5}{7}-\frac{4}{3}\times 2}$$

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

$$\frac{\frac{7}{3}x+\frac{5}{4}}{\frac{5}{7}-\frac{4\times 2}{3}}$$

Multiply 4 and 2 to get 8.

$$\frac{\frac{7}{3}x+\frac{5}{4}}{\frac{5}{7}-\frac{8}{3}}$$

Least common multiple of 7 and 3 is 21. Convert \frac{5}{7} and \frac{8}{3} to fractions with denominator 21.

$$\frac{\frac{7}{3}x+\frac{5}{4}}{\frac{15}{21}-\frac{56}{21}}$$

Since \frac{15}{21} and \frac{56}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{3}x+\frac{5}{4}}{\frac{15-56}{21}}$$

Subtract 56 from 15 to get -41.

$$\frac{\frac{7}{3}x+\frac{5}{4}}{-\frac{41}{21}}$$

Divide \frac{7}{3}x+\frac{5}{4} by -\frac{41}{21} by multiplying \frac{7}{3}x+\frac{5}{4} by the reciprocal of -\frac{41}{21}.

$$\frac{\left(\frac{7}{3}x+\frac{5}{4}\right)\times 21}{-41}$$

Use the distributive property to multiply \frac{7}{3}x+\frac{5}{4} by 21.

$$\frac{\frac{7}{3}x\times 21+\frac{5}{4}\times 21}{-41}$$

Express \frac{7}{3}\times 21 as a single fraction.

$$\frac{\frac{7\times 21}{3}x+\frac{5}{4}\times 21}{-41}$$

Multiply 7 and 21 to get 147.

$$\frac{\frac{147}{3}x+\frac{5}{4}\times 21}{-41}$$

Divide 147 by 3 to get 49.

$$\frac{49x+\frac{5}{4}\times 21}{-41}$$

Express \frac{5}{4}\times 21 as a single fraction.

$$\frac{49x+\frac{5\times 21}{4}}{-41}$$

Multiply 5 and 21 to get 105.

$$\frac{49x+\frac{105}{4}}{-41}$$

Expand

$$-\frac{49x}{41}-\frac{105}{164}$$

Solution Steps

Reduce the fraction \frac{4}{8} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{7}{3}x+\frac{3}{4}+\frac{1}{2}}{\frac{5}{7}-\frac{8}{6}\times \frac{6}{3}}$$

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

$$\frac{\frac{7}{3}x+\frac{3}{4}+\frac{2}{4}}{\frac{5}{7}-\frac{8}{6}\times \frac{6}{3}}$$

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

$$\frac{\frac{7}{3}x+\frac{3+2}{4}}{\frac{5}{7}-\frac{8}{6}\times \frac{6}{3}}$$

Add 3 and 2 to get 5.

$$\frac{\frac{7}{3}x+\frac{5}{4}}{\frac{5}{7}-\frac{8}{6}\times \frac{6}{3}}$$

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{7}{3}x+\frac{5}{4}}{\frac{5}{7}-\frac{4}{3}\times \frac{6}{3}}$$

Divide 6 by 3 to get 2.

$$\frac{\frac{7}{3}x+\frac{5}{4}}{\frac{5}{7}-\frac{4}{3}\times 2}$$

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

$$\frac{\frac{7}{3}x+\frac{5}{4}}{\frac{5}{7}-\frac{4\times 2}{3}}$$

Multiply 4 and 2 to get 8.

$$\frac{\frac{7}{3}x+\frac{5}{4}}{\frac{5}{7}-\frac{8}{3}}$$

Least common multiple of 7 and 3 is 21. Convert \frac{5}{7} and \frac{8}{3} to fractions with denominator 21.

$$\frac{\frac{7}{3}x+\frac{5}{4}}{\frac{15}{21}-\frac{56}{21}}$$

Since \frac{15}{21} and \frac{56}{21} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{3}x+\frac{5}{4}}{\frac{15-56}{21}}$$

Subtract 56 from 15 to get -41.

$$\frac{\frac{7}{3}x+\frac{5}{4}}{-\frac{41}{21}}$$

Divide \frac{7}{3}x+\frac{5}{4} by -\frac{41}{21} by multiplying \frac{7}{3}x+\frac{5}{4} by the reciprocal of -\frac{41}{21}.

$$\frac{\left(\frac{7}{3}x+\frac{5}{4}\right)\times 21}{-41}$$

Use the distributive property to multiply \frac{7}{3}x+\frac{5}{4} by 21.

$$\frac{\frac{7}{3}x\times 21+\frac{5}{4}\times 21}{-41}$$

Express \frac{7}{3}\times 21 as a single fraction.

$$\frac{\frac{7\times 21}{3}x+\frac{5}{4}\times 21}{-41}$$

Multiply 7 and 21 to get 147.

$$\frac{\frac{147}{3}x+\frac{5}{4}\times 21}{-41}$$

Divide 147 by 3 to get 49.

$$\frac{49x+\frac{5}{4}\times 21}{-41}$$

Express \frac{5}{4}\times 21 as a single fraction.

$$\frac{49x+\frac{5\times 21}{4}}{-41}$$

Multiply 5 and 21 to get 105.

$$\frac{49x+\frac{105}{4}}{-41}$$