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

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

Evaluate

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

Short Solution Steps

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

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

Use the distributive property to multiply -x-6 by x+3.

$$\frac{\left(-x\right)x+3\left(-x\right)-6x-18}{\left(6x+9\right)\left(x^{2}-4\right)}$$

Use the distributive property to multiply 6x+9 by x^{2}-4.

$$\frac{\left(-x\right)x+3\left(-x\right)-6x-18}{6x^{3}-24x+9x^{2}-36}$$

Multiply x and x to get x^{2}.

$$\frac{-x^{2}+3\left(-1\right)x-6x-18}{6x^{3}-24x+9x^{2}-36}$$

Multiply 3 and -1 to get -3.

$$\frac{-x^{2}-3x-6x-18}{6x^{3}-24x+9x^{2}-36}$$

Combine -3x and -6x to get -9x.

$$\frac{-x^{2}-9x-18}{6x^{3}-24x+9x^{2}-36}$$

Expand

$$-\frac{x^{2}+9x+18}{3\left(2x+3\right)\left(x^{2}-4\right)}$$

Short Solution Steps

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

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

Use the distributive property to multiply -x-6 by x+3.

$$\frac{\left(-x\right)x+3\left(-x\right)-6x-18}{\left(6x+9\right)\left(x^{2}-4\right)}$$

Use the distributive property to multiply 6x+9 by x^{2}-4.

$$\frac{\left(-x\right)x+3\left(-x\right)-6x-18}{6x^{3}-24x+9x^{2}-36}$$

Multiply x and x to get x^{2}.

$$\frac{-x^{2}+3\left(-1\right)x-6x-18}{6x^{3}-24x+9x^{2}-36}$$

Multiply 3 and -1 to get -3.

$$\frac{-x^{2}-3x-6x-18}{6x^{3}-24x+9x^{2}-36}$$

Combine -3x and -6x to get -9x.

$$\frac{-x^{2}-9x-18}{6x^{3}-24x+9x^{2}-36}$$