Solve 1/1+2-3/frac{4{x}-x}

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

Evaluate

$$-\frac{8x}{3\left(4-x^{2}\right)}$$

Short Solution Steps

Add 1 and 2 to get 3.

$$\frac{\frac{1}{3}-3}{\frac{4}{x}-x}$$

Convert 3 to fraction \frac{9}{3}.

$$\frac{\frac{1}{3}-\frac{9}{3}}{\frac{4}{x}-x}$$

Since \frac{1}{3} and \frac{9}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-9}{3}}{\frac{4}{x}-x}$$

Subtract 9 from 1 to get -8.

$$\frac{-\frac{8}{3}}{\frac{4}{x}-x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.

$$\frac{-\frac{8}{3}}{\frac{4}{x}-\frac{xx}{x}}$$

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

$$\frac{-\frac{8}{3}}{\frac{4-xx}{x}}$$

Do the multiplications in 4-xx.

$$\frac{-\frac{8}{3}}{\frac{4-x^{2}}{x}}$$

Divide -\frac{8}{3} by \frac{4-x^{2}}{x} by multiplying -\frac{8}{3} by the reciprocal of \frac{4-x^{2}}{x}.

$$\frac{-8x}{3\left(4-x^{2}\right)}$$

Use the distributive property to multiply 3 by 4-x^{2}.

$$\frac{-8x}{12-3x^{2}}$$

Expand

$$-\frac{8x}{3\left(4-x^{2}\right)}$$

Short Solution Steps

Add 1 and 2 to get 3.

$$\frac{\frac{1}{3}-3}{\frac{4}{x}-x}$$

Convert 3 to fraction \frac{9}{3}.

$$\frac{\frac{1}{3}-\frac{9}{3}}{\frac{4}{x}-x}$$

Since \frac{1}{3} and \frac{9}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-9}{3}}{\frac{4}{x}-x}$$

Subtract 9 from 1 to get -8.

$$\frac{-\frac{8}{3}}{\frac{4}{x}-x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x}{x}.

$$\frac{-\frac{8}{3}}{\frac{4}{x}-\frac{xx}{x}}$$

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

$$\frac{-\frac{8}{3}}{\frac{4-xx}{x}}$$

Do the multiplications in 4-xx.

$$\frac{-\frac{8}{3}}{\frac{4-x^{2}}{x}}$$

Divide -\frac{8}{3} by \frac{4-x^{2}}{x} by multiplying -\frac{8}{3} by the reciprocal of \frac{4-x^{2}}{x}.

$$\frac{-8x}{3\left(4-x^{2}\right)}$$

Use the distributive property to multiply 3 by 4-x^{2}.

$$\frac{-8x}{12-3x^{2}}$$