Solve E=6/5-3/7/frac{4{3}+1/2}*frac{-frac{1}{2}+frac{4}{3}}{frac{5}{4}-1}

$$E = \frac { \frac { 6 } { 5 } - \frac { 3 } { 7 } } { \frac { 4 } { 3 } + \frac { 1 } { 2 } } \times \frac { - \frac { 1 } { 2 } + \frac { 4 } { 3 } } { \frac { 5 } { 4 } - 1 }$$

Solve for E

$$E = \frac{108}{77} = 1\frac{31}{77} \approx 1.402597403$$

Steps for Solving Linear Equation

Least common multiple of 5 and 7 is 35. Convert \frac{6}{5} and \frac{3}{7} to fractions with denominator 35.

$$E=\frac{\frac{42}{35}-\frac{15}{35}}{\frac{4}{3}+\frac{1}{2}}\times \frac{-\frac{1}{2}+\frac{4}{3}}{\frac{5}{4}-1}$$

Since \frac{42}{35} and \frac{15}{35} have the same denominator, subtract them by subtracting their numerators.

$$E=\frac{\frac{42-15}{35}}{\frac{4}{3}+\frac{1}{2}}\times \frac{-\frac{1}{2}+\frac{4}{3}}{\frac{5}{4}-1}$$

Subtract 15 from 42 to get 27.

$$E=\frac{\frac{27}{35}}{\frac{4}{3}+\frac{1}{2}}\times \frac{-\frac{1}{2}+\frac{4}{3}}{\frac{5}{4}-1}$$

Least common multiple of 3 and 2 is 6. Convert \frac{4}{3} and \frac{1}{2} to fractions with denominator 6.

$$E=\frac{\frac{27}{35}}{\frac{8}{6}+\frac{3}{6}}\times \frac{-\frac{1}{2}+\frac{4}{3}}{\frac{5}{4}-1}$$

Since \frac{8}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$E=\frac{\frac{27}{35}}{\frac{8+3}{6}}\times \frac{-\frac{1}{2}+\frac{4}{3}}{\frac{5}{4}-1}$$

Add 8 and 3 to get 11.

$$E=\frac{\frac{27}{35}}{\frac{11}{6}}\times \frac{-\frac{1}{2}+\frac{4}{3}}{\frac{5}{4}-1}$$

Divide \frac{27}{35} by \frac{11}{6} by multiplying \frac{27}{35} by the reciprocal of \frac{11}{6}.

$$E=\frac{27}{35}\times \frac{6}{11}\times \frac{-\frac{1}{2}+\frac{4}{3}}{\frac{5}{4}-1}$$

Multiply \frac{27}{35} times \frac{6}{11} by multiplying numerator times numerator and denominator times denominator.

$$E=\frac{27\times 6}{35\times 11}\times \frac{-\frac{1}{2}+\frac{4}{3}}{\frac{5}{4}-1}$$

Do the multiplications in the fraction \frac{27\times 6}{35\times 11}.

$$E=\frac{162}{385}\times \frac{-\frac{1}{2}+\frac{4}{3}}{\frac{5}{4}-1}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{4}{3} to fractions with denominator 6.

$$E=\frac{162}{385}\times \frac{-\frac{3}{6}+\frac{8}{6}}{\frac{5}{4}-1}$$

Since -\frac{3}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$E=\frac{162}{385}\times \frac{\frac{-3+8}{6}}{\frac{5}{4}-1}$$

Add -3 and 8 to get 5.

$$E=\frac{162}{385}\times \frac{\frac{5}{6}}{\frac{5}{4}-1}$$

Convert 1 to fraction \frac{4}{4}.

$$E=\frac{162}{385}\times \frac{\frac{5}{6}}{\frac{5}{4}-\frac{4}{4}}$$

Since \frac{5}{4} and \frac{4}{4} have the same denominator, subtract them by subtracting their numerators.

$$E=\frac{162}{385}\times \frac{\frac{5}{6}}{\frac{5-4}{4}}$$

Subtract 4 from 5 to get 1.

$$E=\frac{162}{385}\times \frac{\frac{5}{6}}{\frac{1}{4}}$$

Divide \frac{5}{6} by \frac{1}{4} by multiplying \frac{5}{6} by the reciprocal of \frac{1}{4}.

$$E=\frac{162}{385}\times \frac{5}{6}\times 4$$

Express \frac{5}{6}\times 4 as a single fraction.

$$E=\frac{162}{385}\times \frac{5\times 4}{6}$$

Multiply 5 and 4 to get 20.

$$E=\frac{162}{385}\times \frac{20}{6}$$

Reduce the fraction \frac{20}{6} to lowest terms by extracting and canceling out 2.

$$E=\frac{162}{385}\times \frac{10}{3}$$

Multiply \frac{162}{385} times \frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$E=\frac{162\times 10}{385\times 3}$$

Do the multiplications in the fraction \frac{162\times 10}{385\times 3}.

$$E=\frac{1620}{1155}$$

Reduce the fraction \frac{1620}{1155} to lowest terms by extracting and canceling out 15.

$$E=\frac{108}{77}$$

Assign E

$$E≔\frac{108}{77}$$