Algebra Examples

$\frac{4 n - 8}{n - 2} = n + 2$

Step 1

Factor each term.

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Step 1.1

Factor $4$ out of $4 n - 8$ .

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Step 1.1.1

Factor $4$ out of $4 n$ .

$\frac{4 (n) - 8}{n - 2} = n + 2$

Step 1.1.2

Factor $4$ out of $- 8$ .

$\frac{4 n + 4 \cdot - 2}{n - 2} = n + 2$

Step 1.1.3

Factor $4$ out of $4 n + 4 \cdot - 2$ .

$\frac{4 (n - 2)}{n - 2} = n + 2$

Step 1.2

Reduce the expression by cancelling the common factors.

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Step 1.2.1

Reduce the expression $\frac{4 (n - 2)}{n - 2}$ by cancelling the common factors.

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Step 1.2.1.1

Cancel the common factor.

$\frac{4 (n - 2)}{n - 2} = n + 2$

Step 1.2.1.2

Rewrite the expression.

$\frac{4}{1} = n + 2$

Step 1.2.2

Divide $4$ by $1$ .

$4 = n + 2$

Step 2

Solve the equation.

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Step 2.1

Rewrite the equation as $n + 2 = 4$ .

$n + 2 = 4$

Step 2.2

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

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Step 2.2.1

Subtract $2$ from both sides of the equation.

$n = 4 - 2$

Step 2.2.2

Subtract $2$ from $4$ .

$n = 2$

Step 3

Exclude the solutions that do not make $\frac{4 n - 8}{n - 2} = n + 2$ true.

$No solution$