Solve by Factoring (x^2-7x-18)/(x+2)=x-9

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

Step 1

Move all the expressions to the left side of the equation.

Subtract $x$ from both sides of the equation.

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

Add $9$ to both sides of the equation.

$\frac{x^{2} - 7 x - 18}{x + 2} - x + 9 = 0$

Step 2

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

Simplify each term.

Factor $x^{2} - 7 x - 18$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 18$ and whose sum is $- 7$ .

$- 9, 2$

Write the factored form using these integers.

$\frac{(x - 9) (x + 2)}{x + 2} - x + 9 = 0$

Cancel the common factor of $x + 2$ .

Cancel the common factor.

$\frac{(x - 9) (x + 2)}{x + 2} - x + 9 = 0$

Divide $x - 9$ by $1$ .

$x - 9 - x + 9 = 0$

Combine the opposite terms in $x - 9 - x + 9$ .

Subtract $x$ from $x$ .

$0 - 9 + 9 = 0$

Subtract $9$ from $0$ .

$- 9 + 9 = 0$

Add $- 9$ and $9$ .

$0 = 0$

Step 3

Since $0 = 0$ , the equation will always be true.

Always true

Solve by Factoring (x^2-7x-18)/(x+2)=x-9

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