Solve 2x(-1/2)/-frac{1{2}-1}+2/-frac{1{2}+2}

$$\frac { 2 x ( - \frac { 1 } { 2 } ) } { - \frac { 1 } { 2 } - 1 } + \frac { 2 } { - \frac { 1 } { 2 } + 2 }$$

Factor

$$\frac{2\left(x+2\right)}{3}$$

Solution Steps

Cancel out 2 and 2.

$$factor(\frac{-x}{-\frac{1}{2}-1}+\frac{2}{-\frac{1}{2}+2})$$

Convert 1 to fraction \frac{2}{2}.

$$factor(\frac{-x}{-\frac{1}{2}-\frac{2}{2}}+\frac{2}{-\frac{1}{2}+2})$$

Since -\frac{1}{2} and \frac{2}{2} have the same denominator, subtract them by subtracting their numerators.

$$factor(\frac{-x}{\frac{-1-2}{2}}+\frac{2}{-\frac{1}{2}+2})$$

Subtract 2 from -1 to get -3.

$$factor(\frac{-x}{-\frac{3}{2}}+\frac{2}{-\frac{1}{2}+2})$$

Divide -x by -\frac{3}{2} by multiplying -x by the reciprocal of -\frac{3}{2}.

$$factor(\frac{-x\times 2}{-3}+\frac{2}{-\frac{1}{2}+2})$$

Multiply -1 and 2 to get -2.

$$factor(\frac{-2x}{-3}+\frac{2}{-\frac{1}{2}+2})$$

Convert 2 to fraction \frac{4}{2}.

$$factor(\frac{-2x}{-3}+\frac{2}{-\frac{1}{2}+\frac{4}{2}})$$

Since -\frac{1}{2} and \frac{4}{2} have the same denominator, add them by adding their numerators.

$$factor(\frac{-2x}{-3}+\frac{2}{\frac{-1+4}{2}})$$

Add -1 and 4 to get 3.

$$factor(\frac{-2x}{-3}+\frac{2}{\frac{3}{2}})$$

Divide 2 by \frac{3}{2} by multiplying 2 by the reciprocal of \frac{3}{2}.

$$factor(\frac{-2x}{-3}+2\times \frac{2}{3})$$

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

$$factor(\frac{-2x}{-3}+\frac{2\times 2}{3})$$

Multiply 2 and 2 to get 4.

$$factor(\frac{-2x}{-3}+\frac{4}{3})$$

Factor out \frac{2}{3}.

$$\frac{2\left(x+2\right)}{3}$$

Evaluate

$$\frac{2\left(x+2\right)}{3}$$