Solve 2(-4)^2-4/3(-4)+2/frac{1{2}(-4)+4}

$$\frac { 2 ( - 4 ) ^ { 2 } - 4 / 3 ( - 4 ) + 2 } { \frac { 1 } { 2 } ( - 4 ) + 4 }$$

Evaluate

$$\frac{59}{3}\approx 19.666666667$$

Solution Steps

Calculate -4 to the power of 2 and get 16.

$$\frac{2\times 16-\frac{4}{3}\left(-4\right)+2}{\frac{1}{2}\left(-4\right)+4}$$

Multiply 2 and 16 to get 32.

$$\frac{32-\frac{4}{3}\left(-4\right)+2}{\frac{1}{2}\left(-4\right)+4}$$

Express \frac{4}{3}\left(-4\right) as a single fraction.

$$\frac{32-\frac{4\left(-4\right)}{3}+2}{\frac{1}{2}\left(-4\right)+4}$$

Multiply 4 and -4 to get -16.

$$\frac{32-\frac{-16}{3}+2}{\frac{1}{2}\left(-4\right)+4}$$

Fraction \frac{-16}{3} can be rewritten as -\frac{16}{3} by extracting the negative sign.

$$\frac{32-\left(-\frac{16}{3}\right)+2}{\frac{1}{2}\left(-4\right)+4}$$

The opposite of -\frac{16}{3} is \frac{16}{3}.

$$\frac{32+\frac{16}{3}+2}{\frac{1}{2}\left(-4\right)+4}$$

Convert 32 to fraction \frac{96}{3}.

$$\frac{\frac{96}{3}+\frac{16}{3}+2}{\frac{1}{2}\left(-4\right)+4}$$

Since \frac{96}{3} and \frac{16}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{96+16}{3}+2}{\frac{1}{2}\left(-4\right)+4}$$

Add 96 and 16 to get 112.

$$\frac{\frac{112}{3}+2}{\frac{1}{2}\left(-4\right)+4}$$

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

$$\frac{\frac{112}{3}+\frac{6}{3}}{\frac{1}{2}\left(-4\right)+4}$$

Since \frac{112}{3} and \frac{6}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{112+6}{3}}{\frac{1}{2}\left(-4\right)+4}$$

Add 112 and 6 to get 118.

$$\frac{\frac{118}{3}}{\frac{1}{2}\left(-4\right)+4}$$

Multiply \frac{1}{2} and -4 to get \frac{-4}{2}.

$$\frac{\frac{118}{3}}{\frac{-4}{2}+4}$$

Divide -4 by 2 to get -2.

$$\frac{\frac{118}{3}}{-2+4}$$

Add -2 and 4 to get 2.

$$\frac{\frac{118}{3}}{2}$$

Express \frac{\frac{118}{3}}{2} as a single fraction.

$$\frac{118}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$\frac{118}{6}$$

Reduce the fraction \frac{118}{6} to lowest terms by extracting and canceling out 2.

$$\frac{59}{3}$$

Factor

$$\frac{59}{3} = 19\frac{2}{3} = 19.666666666666668$$