Solve G(3/T)=(1/3)^2-2(3/4)+9/frac{4{3}}

$$G ( \frac { 3 } { T } ) = \frac { ( \frac { 1 } { 3 } ) ^ { 2 } - 2 ( \frac { 3 } { 4 } ) + 9 } { \frac { 4 } { 3 } }$$

Evaluate

$$\frac{137}{24}\approx 5.708333333$$

Solution Steps

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{\frac{1}{9}-2\times \frac{3}{4}+9}{\frac{4}{3}}$$

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

$$\frac{\frac{1}{9}-\frac{2\times 3}{4}+9}{\frac{4}{3}}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{1}{9}-\frac{6}{4}+9}{\frac{4}{3}}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{9}-\frac{3}{2}+9}{\frac{4}{3}}$$

Least common multiple of 9 and 2 is 18. Convert \frac{1}{9} and \frac{3}{2} to fractions with denominator 18.

$$\frac{\frac{2}{18}-\frac{27}{18}+9}{\frac{4}{3}}$$

Since \frac{2}{18} and \frac{27}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2-27}{18}+9}{\frac{4}{3}}$$

Subtract 27 from 2 to get -25.

$$\frac{-\frac{25}{18}+9}{\frac{4}{3}}$$

Convert 9 to fraction \frac{162}{18}.

$$\frac{-\frac{25}{18}+\frac{162}{18}}{\frac{4}{3}}$$

Since -\frac{25}{18} and \frac{162}{18} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-25+162}{18}}{\frac{4}{3}}$$

Add -25 and 162 to get 137.

$$\frac{\frac{137}{18}}{\frac{4}{3}}$$

Divide \frac{137}{18} by \frac{4}{3} by multiplying \frac{137}{18} by the reciprocal of \frac{4}{3}.

$$\frac{137}{18}\times \frac{3}{4}$$

Multiply \frac{137}{18} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{137\times 3}{18\times 4}$$

Do the multiplications in the fraction \frac{137\times 3}{18\times 4}.

$$\frac{411}{72}$$

Reduce the fraction \frac{411}{72} to lowest terms by extracting and canceling out 3.

$$\frac{137}{24}$$

Factor

$$\frac{137}{2 ^ {3} \cdot 3} = 5\frac{17}{24} = 5.708333333333333$$