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

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

Evaluate

$$-\frac{2\left(x-2\right)}{x\left(x+6\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

$$\frac{\frac{2-x}{x}}{\frac{3\times 2}{2}+\frac{x}{2}}$$

Since \frac{3\times 2}{2} and \frac{x}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2-x}{x}}{\frac{3\times 2+x}{2}}$$

Do the multiplications in 3\times 2+x.

$$\frac{\frac{2-x}{x}}{\frac{6+x}{2}}$$

Divide \frac{2-x}{x} by \frac{6+x}{2} by multiplying \frac{2-x}{x} by the reciprocal of \frac{6+x}{2}.

$$\frac{\left(2-x\right)\times 2}{x\left(6+x\right)}$$

Use the distributive property to multiply 2-x by 2.

$$\frac{4-2x}{x\left(6+x\right)}$$

Use the distributive property to multiply x by 6+x.

$$\frac{4-2x}{6x+x^{2}}$$

Expand

$$-\frac{2\left(x-2\right)}{x\left(x+6\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

$$\frac{\frac{2-x}{x}}{\frac{3\times 2}{2}+\frac{x}{2}}$$

Since \frac{3\times 2}{2} and \frac{x}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{2-x}{x}}{\frac{3\times 2+x}{2}}$$

Do the multiplications in 3\times 2+x.

$$\frac{\frac{2-x}{x}}{\frac{6+x}{2}}$$

Divide \frac{2-x}{x} by \frac{6+x}{2} by multiplying \frac{2-x}{x} by the reciprocal of \frac{6+x}{2}.

$$\frac{\left(2-x\right)\times 2}{x\left(6+x\right)}$$

Use the distributive property to multiply 2-x by 2.

$$\frac{4-2x}{x\left(6+x\right)}$$

Use the distributive property to multiply x by 6+x.

$$\frac{4-2x}{6x+x^{2}}$$