Pre-Algebra Examples

$\frac{20}{2 x - 4} + \frac{1}{x - 2} = \frac{11}{2}$

Step 1

Simplify $\frac{20}{2 x - 4} + \frac{1}{x - 2}$ .

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Step 1.1

Cancel the common factor of $20$ and $2 x - 4$ .

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Step 1.1.1

Factor $2$ out of $20$ .

$\frac{2 \cdot 10}{2 x - 4} + \frac{1}{x - 2} = \frac{11}{2}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $2 x$ .

$\frac{2 \cdot 10}{2 (x) - 4} + \frac{1}{x - 2} = \frac{11}{2}$

Step 1.1.2.2

Factor $2$ out of $- 4$ .

$\frac{2 \cdot 10}{2 (x) + 2 (- 2)} + \frac{1}{x - 2} = \frac{11}{2}$

Step 1.1.2.3

Factor $2$ out of $2 (x) + 2 (- 2)$ .

$\frac{2 \cdot 10}{2 (x - 2)} + \frac{1}{x - 2} = \frac{11}{2}$

Step 1.1.2.4

Cancel the common factor.

$\frac{2 \cdot 10}{2 (x - 2)} + \frac{1}{x - 2} = \frac{11}{2}$

Step 1.1.2.5

Rewrite the expression.

$\frac{10}{x - 2} + \frac{1}{x - 2} = \frac{11}{2}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{10 + 1}{x - 2} = \frac{11}{2}$

Step 1.3

Add $10$ and $1$ .

$\frac{11}{x - 2} = \frac{11}{2}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 4$

Step 3