Solve 2x-6/4-4x+x^2div3-x/(x-3)(x+3)

$$\frac { 2 x - 6 } { 4 - 4 x + x ^ { 2 } } \div \frac { 3 - x } { ( x - 3 ) ( x + 3 ) }$$

Evaluate

$$-\frac{2\left(x^{2}-9\right)}{\left(x-2\right)^{2}}$$

Short Solution Steps

Divide \frac{2x-6}{4-4x+x^{2}} by \frac{3-x}{\left(x-3\right)\left(x+3\right)} by multiplying \frac{2x-6}{4-4x+x^{2}} by the reciprocal of \frac{3-x}{\left(x-3\right)\left(x+3\right)}.

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

Extract the negative sign in x-3.

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

Cancel out -x+3 in both numerator and denominator.

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

Use the distributive property to multiply -1 by 2x-6.

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

Use the distributive property to multiply -2x+6 by x+3 and combine like terms.

$$\frac{-2x^{2}+18}{x^{2}-4x+4}$$

Expand

$$-\frac{2\left(x^{2}-9\right)}{x^{2}-4x+4}$$

Short Solution Steps

Divide \frac{2x-6}{4-4x+x^{2}} by \frac{3-x}{\left(x-3\right)\left(x+3\right)} by multiplying \frac{2x-6}{4-4x+x^{2}} by the reciprocal of \frac{3-x}{\left(x-3\right)\left(x+3\right)}.

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

Extract the negative sign in x-3.

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

Cancel out -x+3 in both numerator and denominator.

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

Use the distributive property to multiply -1 by 2x-6.

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

Use the distributive property to multiply -2x+6 by x+3 and combine like terms.

$$\frac{-2x^{2}+18}{x^{2}-4x+4}$$