Algebra Examples

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

Step 1

Subtract $2$ from both sides of the equation.

$\frac{x + 2}{x - 3} - 2 = 0$

Step 2

Simplify $\frac{x + 2}{x - 3} - 2$ .

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Step 2.1

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{x - 3}{x - 3}$ .

$\frac{x + 2}{x - 3} - 2 \cdot \frac{x - 3}{x - 3} = 0$

Step 2.2

Combine $- 2$ and $\frac{x - 3}{x - 3}$ .

$\frac{x + 2}{x - 3} + \frac{- 2 (x - 3)}{x - 3} = 0$

Step 2.3

Combine the numerators over the common denominator.

$\frac{x + 2 - 2 (x - 3)}{x - 3} = 0$

Step 2.4

Simplify the numerator.

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Step 2.4.1

Apply the distributive property.

$\frac{x + 2 - 2 x - 2 \cdot - 3}{x - 3} = 0$

Step 2.4.2

Multiply $- 2$ by $- 3$ .

$\frac{x + 2 - 2 x + 6}{x - 3} = 0$

Step 2.4.3

Subtract $2 x$ from $x$ .

$\frac{- x + 2 + 6}{x - 3} = 0$

Step 2.4.4

Add $2$ and $6$ .

$\frac{- x + 8}{x - 3} = 0$

Step 2.5

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

$\frac{- (x) + 8}{x - 3} = 0$

Step 2.6

Rewrite $8$ as $- 1 (- 8)$ .

$\frac{- (x) - 1 (- 8)}{x - 3} = 0$

Step 2.7

Factor $- 1$ out of $- (x) - 1 (- 8)$ .

$\frac{- (x - 8)}{x - 3} = 0$

Step 2.8

Rewrite $- (x - 8)$ as $- 1 (x - 8)$ .

$\frac{- 1 (x - 8)}{x - 3} = 0$

Step 2.9

Move the negative in front of the fraction.

$- \frac{x - 8}{x - 3} = 0$

Step 3

Set the numerator equal to zero.

$x - 8 = 0$

Step 4

Add $8$ to both sides of the equation.

$x = 8$