Solve -7/x-2+3-2x/x

$$- \frac { 7 } { x - 2 } + \frac { 3 - 2 x } { x }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and x is x\left(x-2\right). Multiply -\frac{7}{x-2} times \frac{x}{x}. Multiply \frac{3-2x}{x} times \frac{x-2}{x-2}.

$$-\frac{7x}{x\left(x-2\right)}+\frac{\left(3-2x\right)\left(x-2\right)}{x\left(x-2\right)}$$

Since -\frac{7x}{x\left(x-2\right)} and \frac{\left(3-2x\right)\left(x-2\right)}{x\left(x-2\right)} have the same denominator, add them by adding their numerators.

$$\frac{-7x+\left(3-2x\right)\left(x-2\right)}{x\left(x-2\right)}$$

Do the multiplications in -7x+\left(3-2x\right)\left(x-2\right).

$$\frac{-7x+3x-6-2x^{2}+4x}{x\left(x-2\right)}$$

Combine like terms in -7x+3x-6-2x^{2}+4x.

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

Expand x\left(x-2\right).

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-2 and x is x\left(x-2\right). Multiply -\frac{7}{x-2} times \frac{x}{x}. Multiply \frac{3-2x}{x} times \frac{x-2}{x-2}.

$$-\frac{7x}{x\left(x-2\right)}+\frac{\left(3-2x\right)\left(x-2\right)}{x\left(x-2\right)}$$

Since -\frac{7x}{x\left(x-2\right)} and \frac{\left(3-2x\right)\left(x-2\right)}{x\left(x-2\right)} have the same denominator, add them by adding their numerators.

$$\frac{-7x+\left(3-2x\right)\left(x-2\right)}{x\left(x-2\right)}$$

Do the multiplications in -7x+\left(3-2x\right)\left(x-2\right).

$$\frac{-7x+3x-6-2x^{2}+4x}{x\left(x-2\right)}$$

Combine like terms in -7x+3x-6-2x^{2}+4x.

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

Expand x\left(x-2\right).

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