Solve 2x^2-18/4-4x+x^2*1/x+3*x^2+x-6/x-3

$$\frac { 2 x ^ { 2 } - 18 } { 4 - 4 x + x ^ { 2 } } \times \frac { 1 } { x + 3 } \cdot \frac { x ^ { 2 } + x - 6 } { x - 3 }$$

Evaluate

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

Short Solution Steps

Multiply \frac{2x^{2}-18}{4-4x+x^{2}} times \frac{1}{x+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2x^{2}-18}{\left(4-4x+x^{2}\right)\left(x+3\right)}\times \frac{x^{2}+x-6}{x-3}$$

Multiply \frac{2x^{2}-18}{\left(4-4x+x^{2}\right)\left(x+3\right)} times \frac{x^{2}+x-6}{x-3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2x^{2}-18\right)\left(x^{2}+x-6\right)}{\left(4-4x+x^{2}\right)\left(x+3\right)\left(x-3\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x-3\right)\left(x-2\right)\left(x+3\right) in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

Multiply \frac{2x^{2}-18}{4-4x+x^{2}} times \frac{1}{x+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2x^{2}-18}{\left(4-4x+x^{2}\right)\left(x+3\right)}\times \frac{x^{2}+x-6}{x-3}$$

Multiply \frac{2x^{2}-18}{\left(4-4x+x^{2}\right)\left(x+3\right)} times \frac{x^{2}+x-6}{x-3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2x^{2}-18\right)\left(x^{2}+x-6\right)}{\left(4-4x+x^{2}\right)\left(x+3\right)\left(x-3\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x-3\right)\left(x-2\right)\left(x+3\right) in both numerator and denominator.

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

Expand the expression.

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