Algebra Examples

$\frac{x^{2} - 11 x + 30}{x - 6} = 1$

Step 1

Factor each term.

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Step 1.1

Factor $x^{2} - 11 x + 30$ 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 $30$ and whose sum is $- 11$ .

$- 6, - 5$

Step 1.1.2

Write the factored form using these integers.

$\frac{(x - 6) (x - 5)}{x - 6} = 1$

Step 1.2

Reduce the expression by cancelling the common factors.

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Step 1.2.1

Reduce the expression $\frac{(x - 6) (x - 5)}{x - 6}$ by cancelling the common factors.

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Step 1.2.1.1

Cancel the common factor.

$\frac{(x - 6) (x - 5)}{x - 6} = 1$

Step 1.2.1.2

Rewrite the expression.

$\frac{x - 5}{1} = 1$

Step 1.2.2

Divide $x - 5$ by $1$ .

$x - 5 = 1$

Step 2

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

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Step 2.1

Add $5$ to both sides of the equation.

$x = 1 + 5$

Step 2.2

Add $1$ and $5$ .

$x = 6$

Step 3

Exclude the solutions that do not make $\frac{x^{2} - 11 x + 30}{x - 6} = 1$ true.

$No solution$