Algebra Examples

$\frac{7}{3 x - 12} - \frac{1}{x - 4} = \frac{2}{3}$

Step 1

Subtract $\frac{2}{3}$ from both sides of the equation.

$\frac{7}{3 x - 12} - \frac{1}{x - 4} - \frac{2}{3} = 0$

Step 2

Simplify $\frac{7}{3 x - 12} - \frac{1}{x - 4} - \frac{2}{3}$ .

Tap for more steps...

Step 2.1

Factor $3$ out of $3 x - 12$ .

Tap for more steps...

Step 2.1.1

Factor $3$ out of $3 x$ .

$\frac{7}{3 (x) - 12} - \frac{1}{x - 4} - \frac{2}{3} = 0$

Step 2.1.2

Factor $3$ out of $- 12$ .

$\frac{7}{3 x + 3 \cdot - 4} - \frac{1}{x - 4} - \frac{2}{3} = 0$

Step 2.1.3

Factor $3$ out of $3 x + 3 \cdot - 4$ .

$\frac{7}{3 (x - 4)} - \frac{1}{x - 4} - \frac{2}{3} = 0$

Step 2.2

Find the common denominator.

Tap for more steps...

Step 2.2.1

Multiply $\frac{1}{x - 4}$ by $\frac{3}{3}$ .

$\frac{7}{3 (x - 4)} - (\frac{1}{x - 4} \cdot \frac{3}{3}) - \frac{2}{3} = 0$

Step 2.2.2

Multiply $\frac{1}{x - 4}$ by $\frac{3}{3}$ .

$\frac{7}{3 (x - 4)} - \frac{3}{(x - 4) \cdot 3} - \frac{2}{3} = 0$

Step 2.2.3

Multiply $\frac{2}{3}$ by $\frac{x - 4}{x - 4}$ .

$\frac{7}{3 (x - 4)} - \frac{3}{(x - 4) \cdot 3} - (\frac{2}{3} \cdot \frac{x - 4}{x - 4}) = 0$

Step 2.2.4

Multiply $\frac{2}{3}$ by $\frac{x - 4}{x - 4}$ .

$\frac{7}{3 (x - 4)} - \frac{3}{(x - 4) \cdot 3} - \frac{2 (x - 4)}{3 (x - 4)} = 0$

Step 2.2.5

Reorder the factors of $(x - 4) \cdot 3$ .

$\frac{7}{3 (x - 4)} - \frac{3}{3 (x - 4)} - \frac{2 (x - 4)}{3 (x - 4)} = 0$

Step 2.3

Combine the numerators over the common denominator.

$\frac{7}{3 (x - 4)} + \frac{- 3 - 2 (x - 4)}{3 (x - 4)} = 0$

Step 2.4

Simplify each term.

Tap for more steps...

Step 2.4.1

Apply the distributive property.

$\frac{7}{3 (x - 4)} + \frac{- 3 - 2 x - 2 \cdot - 4}{3 (x - 4)} = 0$

Step 2.4.2

Multiply $- 2$ by $- 4$ .

$\frac{7}{3 (x - 4)} + \frac{- 3 - 2 x + 8}{3 (x - 4)} = 0$

Step 2.5

Add $- 3$ and $8$ .

$\frac{7}{3 (x - 4)} + \frac{- 2 x + 5}{3 (x - 4)} = 0$

Step 2.6

Combine the numerators over the common denominator.

$\frac{7 - 2 x + 5}{3 (x - 4)} = 0$

Step 2.7

Add $7$ and $5$ .

$\frac{- 2 x + 12}{3 (x - 4)} = 0$

Step 2.8

Factor $2$ out of $- 2 x + 12$ .

Tap for more steps...

Step 2.8.1

Factor $2$ out of $- 2 x$ .

$\frac{2 (- x) + 12}{3 (x - 4)} = 0$

Step 2.8.2

Factor $2$ out of $12$ .

$\frac{2 (- x) + 2 (6)}{3 (x - 4)} = 0$

Step 2.8.3

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

$\frac{2 (- x + 6)}{3 (x - 4)} = 0$

Step 2.9

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

$\frac{2 (- (x) + 6)}{3 (x - 4)} = 0$

Step 2.10

Rewrite $6$ as $- 1 (- 6)$ .

$\frac{2 (- (x) - 1 (- 6))}{3 (x - 4)} = 0$

Step 2.11

Factor $- 1$ out of $- (x) - 1 (- 6)$ .

$\frac{2 (- (x - 6))}{3 (x - 4)} = 0$

Step 2.12

Rewrite $- (x - 6)$ as $- 1 (x - 6)$ .

$\frac{2 (- 1 (x - 6))}{3 (x - 4)} = 0$

Step 2.13

Move the negative in front of the fraction.

$- \frac{2 (x - 6)}{3 (x - 4)} = 0$

Step 3

Set the numerator equal to zero.

$2 (x - 6) = 0$

Step 4

Solve the equation for $x$ .

Tap for more steps...

Step 4.1

Divide each term in $2 (x - 6) = 0$ by $2$ and simplify.

Tap for more steps...

Step 4.1.1

Divide each term in $2 (x - 6) = 0$ by $2$ .

$\frac{2 (x - 6)}{2} = \frac{0}{2}$

Step 4.1.2

Simplify the left side.

Tap for more steps...

Step 4.1.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.1.2.1.1

Cancel the common factor.

$\frac{2 (x - 6)}{2} = \frac{0}{2}$

Step 4.1.2.1.2

Divide $x - 6$ by $1$ .

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

Step 4.1.3

Simplify the right side.

Tap for more steps...

Step 4.1.3.1

Divide $0$ by $2$ .

$x - 6 = 0$

Step 4.2

Add $6$ to both sides of the equation.

$x = 6$