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

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

Evaluate

$$-12$$

Short Solution Steps

Express 6\times \frac{2x-6}{4-4x+x^{2}} as a single fraction.

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

Express \frac{\frac{6\left(2x-6\right)}{4-4x+x^{2}}}{x+3} as a single fraction.

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

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

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

Express \frac{6\left(2x-6\right)\left(x^{2}+x-6\right)}{\left(4-4x+x^{2}\right)\left(x+3\right)\left(3-x\right)}\left(x-2\right) as a single fraction.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -3+x.

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

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

$$-2\times 6$$

Multiply -2 and 6 to get -12.

$$-12$$

Factor

$$-12$$