Solve D=7/4-1/3/frac{2{7}+1/4}divfrac{frac{1}{3}+frac{3}{2}}{frac{8}{3}-frac{3}{2}}

$$D = \frac { \frac { 7 } { 4 } - \frac { 1 } { 3 } } { \frac { 2 } { 7 } + \frac { 1 } { 4 } } \div \frac { \frac { 1 } { 3 } + \frac { 3 } { 2 } } { \frac { 8 } { 3 } - \frac { 3 } { 2 } }$$

Solve for D

$$D = \frac{833}{495} = 1\frac{338}{495} \approx 1.682828283$$

Steps for Solving Linear Equation

Divide \frac{\frac{7}{4}-\frac{1}{3}}{\frac{2}{7}+\frac{1}{4}} by \frac{\frac{1}{3}+\frac{3}{2}}{\frac{8}{3}-\frac{3}{2}} by multiplying \frac{\frac{7}{4}-\frac{1}{3}}{\frac{2}{7}+\frac{1}{4}} by the reciprocal of \frac{\frac{1}{3}+\frac{3}{2}}{\frac{8}{3}-\frac{3}{2}}.

$$D=\frac{\left(\frac{7}{4}-\frac{1}{3}\right)\left(\frac{8}{3}-\frac{3}{2}\right)}{\left(\frac{2}{7}+\frac{1}{4}\right)\left(\frac{1}{3}+\frac{3}{2}\right)}$$

Least common multiple of 4 and 3 is 12. Convert \frac{7}{4} and \frac{1}{3} to fractions with denominator 12.

$$D=\frac{\left(\frac{21}{12}-\frac{4}{12}\right)\left(\frac{8}{3}-\frac{3}{2}\right)}{\left(\frac{2}{7}+\frac{1}{4}\right)\left(\frac{1}{3}+\frac{3}{2}\right)}$$

Since \frac{21}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$D=\frac{\frac{21-4}{12}\left(\frac{8}{3}-\frac{3}{2}\right)}{\left(\frac{2}{7}+\frac{1}{4}\right)\left(\frac{1}{3}+\frac{3}{2}\right)}$$

Subtract 4 from 21 to get 17.

$$D=\frac{\frac{17}{12}\left(\frac{8}{3}-\frac{3}{2}\right)}{\left(\frac{2}{7}+\frac{1}{4}\right)\left(\frac{1}{3}+\frac{3}{2}\right)}$$

Least common multiple of 3 and 2 is 6. Convert \frac{8}{3} and \frac{3}{2} to fractions with denominator 6.

$$D=\frac{\frac{17}{12}\left(\frac{16}{6}-\frac{9}{6}\right)}{\left(\frac{2}{7}+\frac{1}{4}\right)\left(\frac{1}{3}+\frac{3}{2}\right)}$$

Since \frac{16}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.

$$D=\frac{\frac{17}{12}\times \frac{16-9}{6}}{\left(\frac{2}{7}+\frac{1}{4}\right)\left(\frac{1}{3}+\frac{3}{2}\right)}$$

Subtract 9 from 16 to get 7.

$$D=\frac{\frac{17}{12}\times \frac{7}{6}}{\left(\frac{2}{7}+\frac{1}{4}\right)\left(\frac{1}{3}+\frac{3}{2}\right)}$$

Multiply \frac{17}{12} times \frac{7}{6} by multiplying numerator times numerator and denominator times denominator.

$$D=\frac{\frac{17\times 7}{12\times 6}}{\left(\frac{2}{7}+\frac{1}{4}\right)\left(\frac{1}{3}+\frac{3}{2}\right)}$$

Do the multiplications in the fraction \frac{17\times 7}{12\times 6}.

$$D=\frac{\frac{119}{72}}{\left(\frac{2}{7}+\frac{1}{4}\right)\left(\frac{1}{3}+\frac{3}{2}\right)}$$

Least common multiple of 7 and 4 is 28. Convert \frac{2}{7} and \frac{1}{4} to fractions with denominator 28.

$$D=\frac{\frac{119}{72}}{\left(\frac{8}{28}+\frac{7}{28}\right)\left(\frac{1}{3}+\frac{3}{2}\right)}$$

Since \frac{8}{28} and \frac{7}{28} have the same denominator, add them by adding their numerators.

$$D=\frac{\frac{119}{72}}{\frac{8+7}{28}\left(\frac{1}{3}+\frac{3}{2}\right)}$$

Add 8 and 7 to get 15.

$$D=\frac{\frac{119}{72}}{\frac{15}{28}\left(\frac{1}{3}+\frac{3}{2}\right)}$$

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

$$D=\frac{\frac{119}{72}}{\frac{15}{28}\left(\frac{2}{6}+\frac{9}{6}\right)}$$

Since \frac{2}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$D=\frac{\frac{119}{72}}{\frac{15}{28}\times \frac{2+9}{6}}$$

Add 2 and 9 to get 11.

$$D=\frac{\frac{119}{72}}{\frac{15}{28}\times \frac{11}{6}}$$

Multiply \frac{15}{28} times \frac{11}{6} by multiplying numerator times numerator and denominator times denominator.

$$D=\frac{\frac{119}{72}}{\frac{15\times 11}{28\times 6}}$$

Do the multiplications in the fraction \frac{15\times 11}{28\times 6}.

$$D=\frac{\frac{119}{72}}{\frac{165}{168}}$$

Reduce the fraction \frac{165}{168} to lowest terms by extracting and canceling out 3.

$$D=\frac{\frac{119}{72}}{\frac{55}{56}}$$

Divide \frac{119}{72} by \frac{55}{56} by multiplying \frac{119}{72} by the reciprocal of \frac{55}{56}.

$$D=\frac{119}{72}\times \frac{56}{55}$$

Multiply \frac{119}{72} times \frac{56}{55} by multiplying numerator times numerator and denominator times denominator.

$$D=\frac{119\times 56}{72\times 55}$$

Do the multiplications in the fraction \frac{119\times 56}{72\times 55}.

$$D=\frac{6664}{3960}$$

Reduce the fraction \frac{6664}{3960} to lowest terms by extracting and canceling out 8.

$$D=\frac{833}{495}$$

Assign D

$$D≔\frac{833}{495}$$