Solve U=5+3+9/2-3/7/3-frac{9{2}+3/7}

$$U = 5 + \frac { 3 + \frac { 9 } { 2 } - \frac { 3 } { 7 } } { 3 - \frac { 9 } { 2 } + \frac { 3 } { 7 } }$$

Solve for U

$$U = -\frac{8}{5} = -1\frac{3}{5} = -1.6$$

Steps for Solving Linear Equation

Convert 3 to fraction \frac{6}{2}.

$$U=5+\frac{\frac{6}{2}+\frac{9}{2}-\frac{3}{7}}{3-\frac{9}{2}+\frac{3}{7}}$$

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

$$U=5+\frac{\frac{6+9}{2}-\frac{3}{7}}{3-\frac{9}{2}+\frac{3}{7}}$$

Add 6 and 9 to get 15.

$$U=5+\frac{\frac{15}{2}-\frac{3}{7}}{3-\frac{9}{2}+\frac{3}{7}}$$

Least common multiple of 2 and 7 is 14. Convert \frac{15}{2} and \frac{3}{7} to fractions with denominator 14.

$$U=5+\frac{\frac{105}{14}-\frac{6}{14}}{3-\frac{9}{2}+\frac{3}{7}}$$

Since \frac{105}{14} and \frac{6}{14} have the same denominator, subtract them by subtracting their numerators.

$$U=5+\frac{\frac{105-6}{14}}{3-\frac{9}{2}+\frac{3}{7}}$$

Subtract 6 from 105 to get 99.

$$U=5+\frac{\frac{99}{14}}{3-\frac{9}{2}+\frac{3}{7}}$$

Convert 3 to fraction \frac{6}{2}.

$$U=5+\frac{\frac{99}{14}}{\frac{6}{2}-\frac{9}{2}+\frac{3}{7}}$$

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

$$U=5+\frac{\frac{99}{14}}{\frac{6-9}{2}+\frac{3}{7}}$$

Subtract 9 from 6 to get -3.

$$U=5+\frac{\frac{99}{14}}{-\frac{3}{2}+\frac{3}{7}}$$

Least common multiple of 2 and 7 is 14. Convert -\frac{3}{2} and \frac{3}{7} to fractions with denominator 14.

$$U=5+\frac{\frac{99}{14}}{-\frac{21}{14}+\frac{6}{14}}$$

Since -\frac{21}{14} and \frac{6}{14} have the same denominator, add them by adding their numerators.

$$U=5+\frac{\frac{99}{14}}{\frac{-21+6}{14}}$$

Add -21 and 6 to get -15.

$$U=5+\frac{\frac{99}{14}}{-\frac{15}{14}}$$

Divide \frac{99}{14} by -\frac{15}{14} by multiplying \frac{99}{14} by the reciprocal of -\frac{15}{14}.

$$U=5+\frac{99}{14}\left(-\frac{14}{15}\right)$$

Multiply \frac{99}{14} times -\frac{14}{15} by multiplying numerator times numerator and denominator times denominator.

$$U=5+\frac{99\left(-14\right)}{14\times 15}$$

Do the multiplications in the fraction \frac{99\left(-14\right)}{14\times 15}.

$$U=5+\frac{-1386}{210}$$

Reduce the fraction \frac{-1386}{210} to lowest terms by extracting and canceling out 42.

$$U=5-\frac{33}{5}$$

Convert 5 to fraction \frac{25}{5}.

$$U=\frac{25}{5}-\frac{33}{5}$$

Since \frac{25}{5} and \frac{33}{5} have the same denominator, subtract them by subtracting their numerators.

$$U=\frac{25-33}{5}$$

Subtract 33 from 25 to get -8.

$$U=-\frac{8}{5}$$

Assign U

$$U≔-\frac{8}{5}$$