Solve x^2-9/x^2-4x-45*x-6/-3-x

$$\frac { x ^ { 2 } - 9 } { x ^ { 2 } - 4 x - 45 } \cdot \frac { x - 6 } { - 3 - x }$$

Evaluate

$$-\frac{\left(x-6\right)\left(x-3\right)}{\left(x-9\right)\left(x+5\right)}$$

Short Solution Steps

Multiply \frac{x^{2}-9}{x^{2}-4x-45} times \frac{x-6}{-3-x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-9\right)\left(x-6\right)}{\left(x^{2}-4x-45\right)\left(-3-x\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-6\right)\left(x-3\right)\left(x+3\right)}{\left(x-9\right)\left(-x-3\right)\left(x+5\right)}$$

Extract the negative sign in 3+x.

$$\frac{-\left(x-6\right)\left(x-3\right)\left(-x-3\right)}{\left(x-9\right)\left(-x-3\right)\left(x+5\right)}$$

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

$$\frac{-\left(x-6\right)\left(x-3\right)}{\left(x-9\right)\left(x+5\right)}$$

Expand the expression.

$$\frac{-x^{2}+9x-18}{x^{2}-4x-45}$$

Expand

$$-\frac{x^{2}-9x+18}{x^{2}-4x-45}$$

Short Solution Steps

Multiply \frac{x^{2}-9}{x^{2}-4x-45} times \frac{x-6}{-3-x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-9\right)\left(x-6\right)}{\left(x^{2}-4x-45\right)\left(-3-x\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x-6\right)\left(x-3\right)\left(x+3\right)}{\left(x-9\right)\left(-x-3\right)\left(x+5\right)}$$

Extract the negative sign in 3+x.

$$\frac{-\left(x-6\right)\left(x-3\right)\left(-x-3\right)}{\left(x-9\right)\left(-x-3\right)\left(x+5\right)}$$

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

$$\frac{-\left(x-6\right)\left(x-3\right)}{\left(x-9\right)\left(x+5\right)}$$

Expand the expression.

$$\frac{-x^{2}+9x-18}{x^{2}-4x-45}$$