Algebra Examples

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

Step 1

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

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Step 1.1

Subtract $x$ from both sides of the equation.

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

Step 1.2

Add $9$ to both sides of the equation.

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

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 $- 7$ .

$- 9, 2$

Step 2.1.1.2

Write the factored form using these integers.

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

Step 2.1.2

Cancel the common factor of $x + 2$ .

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Step 2.1.2.1

Cancel the common factor.

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

Step 2.1.2.2

Divide $x - 9$ by $1$ .

$x - 9 - x + 9 = 0$

Step 2.2

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

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Step 2.2.1

Subtract $x$ from $x$ .

$0 - 9 + 9 = 0$

Step 2.2.2

Subtract $9$ from $0$ .

$- 9 + 9 = 0$

Step 2.2.3

Add $- 9$ and $9$ .

$0 = 0$

Step 3

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

Always true