Algebra Examples

$\frac{x^{2} - 8 x + 15}{x - 5} = 2$

Step 1

Factor each term.

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Step 1.1

Factor $x^{2} - 8 x + 15$ using the AC method.

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Step 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 $15$ and whose sum is $- 8$ .

$- 5, - 3$

Step 1.1.2

Write the factored form using these integers.

$\frac{(x - 5) (x - 3)}{x - 5} = 2$

Step 1.2

Reduce the expression by cancelling the common factors.

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Step 1.2.1

Reduce the expression $\frac{(x - 5) (x - 3)}{x - 5}$ by cancelling the common factors.

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Step 1.2.1.1

Cancel the common factor.

$\frac{(x - 5) (x - 3)}{x - 5} = 2$

Step 1.2.1.2

Rewrite the expression.

$\frac{x - 3}{1} = 2$

Step 1.2.2

Divide $x - 3$ by $1$ .

$x - 3 = 2$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Add $3$ to both sides of the equation.

$x = 2 + 3$

Step 2.2

Add $2$ and $3$ .

$x = 5$

Step 3

Exclude the solutions that do not make $\frac{x^{2} - 8 x + 15}{x - 5} = 2$ true.

$No solution$