Solve by Factoring 15/4=6/x+3

$\frac{15}{4} = \frac{6}{x} + 3$

Step 1

Move all the expressions to the left side of the equation.

Subtract $\frac{6}{x}$ from both sides of the equation.

$\frac{15}{4} - \frac{6}{x} = 3$

Subtract $3$ from both sides of the equation.

$\frac{15}{4} - \frac{6}{x} - 3 = 0$

Step 2

Simplify $\frac{15}{4} - \frac{6}{x} - 3$ .

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

$- \frac{6}{x} + \frac{15}{4} - 3 \cdot \frac{4}{4} = 0$

Combine $- 3$ and $\frac{4}{4}$ .

$- \frac{6}{x} + \frac{15}{4} + \frac{- 3 \cdot 4}{4} = 0$

Combine the numerators over the common denominator.

$- \frac{6}{x} + \frac{15 - 3 \cdot 4}{4} = 0$

Simplify the numerator.

Multiply $- 3$ by $4$ .

$- \frac{6}{x} + \frac{15 - 12}{4} = 0$

Subtract $12$ from $15$ .

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

Step 3

To write $- \frac{6}{x}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{6}{x} \cdot \frac{4}{4} + \frac{3}{4} = 0$

Step 4

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

$- \frac{6}{x} \cdot \frac{4}{4} + \frac{3}{4} \cdot \frac{x}{x} = 0$

Step 5

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

Multiply $\frac{6}{x}$ by $\frac{4}{4}$ .

$- \frac{6 \cdot 4}{x \cdot 4} + \frac{3}{4} \cdot \frac{x}{x} = 0$

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

$- \frac{6 \cdot 4}{x \cdot 4} + \frac{3 x}{4 x} = 0$

Reorder the factors of $x \cdot 4$ .

$- \frac{6 \cdot 4}{4 x} + \frac{3 x}{4 x} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{- 6 \cdot 4 + 3 x}{4 x} = 0$

Step 7

Simplify the numerator.

Factor $3$ out of $- 6 \cdot 4 + 3 x$ .

Factor $3$ out of $- 6 \cdot 4$ .

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

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $3 (- 2 \cdot 4) + 3 (x)$ .

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

Multiply $- 2$ by $4$ .

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

Step 8

Set the numerator equal to zero.

$3 (- 8 + x) = 0$

Step 9

Solve the equation for $x$ .

Divide each term in $3 (- 8 + x) = 0$ by $3$ and simplify.

Divide each term in $3 (- 8 + x) = 0$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $- 8 + x$ by $1$ .

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

Simplify the right side.

Divide $0$ by $3$ .

$- 8 + x = 0$

Add $8$ to both sides of the equation.

$x = 8$

Solve by Factoring 15/4=6/x+3

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