Solve by Factoring 6/8=12/x

$\frac{6}{8} = \frac{12}{x}$

Step 1

Subtract $\frac{12}{x}$ from both sides of the equation.

$\frac{6}{8} - \frac{12}{x} = 0$

Step 2

Cancel the common factor of $6$ and $8$ .

Factor $2$ out of $6$ .

$\frac{2 (3)}{8} - \frac{12}{x} = 0$

Cancel the common factors.

Factor $2$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{3}{4} \cdot \frac{x}{x} - \frac{12}{x} = 0$

Step 4

To write $- \frac{12}{x}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3}{4} \cdot \frac{x}{x} - \frac{12}{x} \cdot \frac{4}{4} = 0$

Step 5

Write each expression with a common denominator of $4 x$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{3 x}{4 x} - \frac{12}{x} \cdot \frac{4}{4} = 0$

Multiply $\frac{12}{x}$ by $\frac{4}{4}$ .

$\frac{3 x}{4 x} - \frac{12 \cdot 4}{x \cdot 4} = 0$

Reorder the factors of $x \cdot 4$ .

$\frac{3 x}{4 x} - \frac{12 \cdot 4}{4 x} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{3 x - 12 \cdot 4}{4 x} = 0$

Step 7

Simplify the numerator.

Factor $3$ out of $3 x - 12 \cdot 4$ .

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $- 12 \cdot 4$ .

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

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

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

Multiply $- 4$ by $4$ .

$\frac{3 (x - 16)}{4 x} = 0$

Step 8

Set the numerator equal to zero.

$3 (x - 16) = 0$

Step 9

Solve the equation for $x$ .

Divide each term in $3 (x - 16) = 0$ by $3$ and simplify.

Divide each term in $3 (x - 16) = 0$ by $3$ .

$\frac{3 (x - 16)}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (x - 16)}{3} = \frac{0}{3}$

Divide $x - 16$ by $1$ .

$x - 16 = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$x - 16 = 0$

Add $16$ to both sides of the equation.

$x = 16$

Solve by Factoring 6/8=12/x

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