Solve frac{9x^{2}-4}{x^2-4x}*4x^2-x^3/3x^2+10x-8

$$\frac { 9 x ^ { 2 } - 4 } { x ^ { 2 } - 4 x } \cdot \frac { 4 x ^ { 2 } - x ^ { 3 } } { 3 x ^ { 2 } + 10 x - 8 }$$

Evaluate

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

Short Solution Steps

Multiply \frac{9x^{2}-4}{x^{2}-4x} times \frac{4x^{2}-x^{3}}{3x^{2}+10x-8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(9x^{2}-4\right)\left(4x^{2}-x^{3}\right)}{\left(x^{2}-4x\right)\left(3x^{2}+10x-8\right)}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in 4-x.

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

Cancel out x\left(x-4\right)\left(3x-2\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{-3x^{2}-2x}{x+4}$$

Expand

$$-\frac{3x^{2}+2x}{x+4}$$

Short Solution Steps

Multiply \frac{9x^{2}-4}{x^{2}-4x} times \frac{4x^{2}-x^{3}}{3x^{2}+10x-8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(9x^{2}-4\right)\left(4x^{2}-x^{3}\right)}{\left(x^{2}-4x\right)\left(3x^{2}+10x-8\right)}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in 4-x.

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

Cancel out x\left(x-4\right)\left(3x-2\right) in both numerator and denominator.

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

Expand the expression.

$$\frac{-3x^{2}-2x}{x+4}$$