Solve x^2-7x-18/x+2=x-9

$$\frac{ { x }^{ 2 } -7x-18 }{ x+2 } =x-9$$

Solve for x

$$x\neq -2$$

Solution Steps

Variable x cannot be equal to -2 since division by zero is not defined. Multiply both sides of the equation by x+2.

$$x^{2}-7x-18=\left(x+2\right)x+\left(x+2\right)\left(-9\right)$$

Use the distributive property to multiply x+2 by x.

$$x^{2}-7x-18=x^{2}+2x+\left(x+2\right)\left(-9\right)$$

Use the distributive property to multiply x+2 by -9.

$$x^{2}-7x-18=x^{2}+2x-9x-18$$

Combine 2x and -9x to get -7x.

$$x^{2}-7x-18=x^{2}-7x-18$$

Subtract x^{2} from both sides.

$$x^{2}-7x-18-x^{2}=-7x-18$$

Combine x^{2} and -x^{2} to get 0.

$$-7x-18=-7x-18$$

Add 7x to both sides.

$$-7x-18+7x=-18$$

Combine -7x and 7x to get 0.

$$-18=-18$$

Compare -18 and -18.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$

Variable x cannot be equal to -2.

$$x\in \mathrm{R}\setminus -2$$