Pre-Algebra Examples

$\frac{12}{x - 5} - 2 = \frac{4 (x - 2)}{x - 5}$

Step 1

Simplify $\frac{12}{x - 5} - 2$ .

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Step 1.1

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{x - 5}{x - 5}$ .

$\frac{12}{x - 5} - 2 \cdot \frac{x - 5}{x - 5} = \frac{4 (x - 2)}{x - 5}$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $- 2$ and $\frac{x - 5}{x - 5}$ .

$\frac{12}{x - 5} + \frac{- 2 (x - 5)}{x - 5} = \frac{4 (x - 2)}{x - 5}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{12 - 2 (x - 5)}{x - 5} = \frac{4 (x - 2)}{x - 5}$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Factor $2$ out of $12 - 2 (x - 5)$ .

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Step 1.3.1.1

Factor $2$ out of $12$ .

$\frac{2 (6) - 2 (x - 5)}{x - 5} = \frac{4 (x - 2)}{x - 5}$

Step 1.3.1.2

Factor $2$ out of $- 2 (x - 5)$ .

$\frac{2 (6) + 2 (- (x - 5))}{x - 5} = \frac{4 (x - 2)}{x - 5}$

Step 1.3.1.3

Factor $2$ out of $2 (6) + 2 (- (x - 5))$ .

$\frac{2 (6 - (x - 5))}{x - 5} = \frac{4 (x - 2)}{x - 5}$

Step 1.3.2

Apply the distributive property.

$\frac{2 (6 - x - - 5)}{x - 5} = \frac{4 (x - 2)}{x - 5}$

Step 1.3.3

Multiply $- 1$ by $- 5$ .

$\frac{2 (6 - x + 5)}{x - 5} = \frac{4 (x - 2)}{x - 5}$

Step 1.3.4

Add $6$ and $5$ .

$\frac{2 (- x + 11)}{x - 5} = \frac{4 (x - 2)}{x - 5}$

Step 1.4

Simplify with factoring out.

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Step 1.4.1

Factor $- 1$ out of $- x$ .

$\frac{2 (- (x) + 11)}{x - 5} = \frac{4 (x - 2)}{x - 5}$

Step 1.4.2

Rewrite $11$ as $- 1 (- 11)$ .

$\frac{2 (- (x) - 1 (- 11))}{x - 5} = \frac{4 (x - 2)}{x - 5}$

Step 1.4.3

Factor $- 1$ out of $- (x) - 1 (- 11)$ .

$\frac{2 (- (x - 11))}{x - 5} = \frac{4 (x - 2)}{x - 5}$

Step 1.4.4

Simplify the expression.

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Step 1.4.4.1

Rewrite $- (x - 11)$ as $- 1 (x - 11)$ .

$\frac{2 (- 1 (x - 11))}{x - 5} = \frac{4 (x - 2)}{x - 5}$

Step 1.4.4.2

Move the negative in front of the fraction.

$- \frac{2 (x - 11)}{x - 5} = \frac{4 (x - 2)}{x - 5}$

Step 2

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

No solution

Step 3