Solve by Factoring 3/2=3/(2x)-6/(5x)

$\frac{3}{2} = \frac{3}{2 x} - \frac{6}{5 x}$

Step 1

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

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

$\frac{3}{2} - \frac{3}{2 x} = - \frac{6}{5 x}$

Add $\frac{6}{5 x}$ to both sides of the equation.

$\frac{3}{2} - \frac{3}{2 x} + \frac{6}{5 x} = 0$

Step 2

Simplify $\frac{3}{2} - \frac{3}{2 x} + \frac{6}{5 x}$ .

To write $- \frac{3}{2 x}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3}{2} - \frac{3}{2 x} \cdot \frac{5}{5} + \frac{6}{5 x} = 0$

To write $\frac{6}{5 x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3}{2} - \frac{3}{2 x} \cdot \frac{5}{5} + \frac{6}{5 x} \cdot \frac{2}{2} = 0$

Write each expression with a common denominator of $10 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{2 x}$ by $\frac{5}{5}$ .

$\frac{3}{2} - \frac{3 \cdot 5}{2 x \cdot 5} + \frac{6}{5 x} \cdot \frac{2}{2} = 0$

Multiply $5$ by $2$ .

$\frac{3}{2} - \frac{3 \cdot 5}{10 x} + \frac{6}{5 x} \cdot \frac{2}{2} = 0$

Multiply $\frac{6}{5 x}$ by $\frac{2}{2}$ .

$\frac{3}{2} - \frac{3 \cdot 5}{10 x} + \frac{6 \cdot 2}{5 x \cdot 2} = 0$

Multiply $2$ by $5$ .

$\frac{3}{2} - \frac{3 \cdot 5}{10 x} + \frac{6 \cdot 2}{10 x} = 0$

Combine the numerators over the common denominator.

$\frac{3}{2} + \frac{- 3 \cdot 5 + 6 \cdot 2}{10 x} = 0$

Simplify the numerator.

Multiply $- 3$ by $5$ .

$\frac{3}{2} + \frac{- 15 + 6 \cdot 2}{10 x} = 0$

Multiply $6$ by $2$ .

$\frac{3}{2} + \frac{- 15 + 12}{10 x} = 0$

Add $- 15$ and $12$ .

$\frac{3}{2} + \frac{- 3}{10 x} = 0$

Move the negative in front of the fraction.

$\frac{3}{2} - \frac{3}{10 x} = 0$

Step 3

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{5 x}{5 x}$ .

$\frac{3}{2} \cdot \frac{5 x}{5 x} - \frac{3}{10 x} = 0$

Step 4

Write each expression with a common denominator of $10 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{2}$ by $\frac{5 x}{5 x}$ .

$\frac{3 (5 x)}{2 (5 x)} - \frac{3}{10 x} = 0$

Multiply $5$ by $2$ .

$\frac{3 (5 x)}{10 x} - \frac{3}{10 x} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{3 (5 x) - 3}{10 x} = 0$

Step 6

Remove parentheses.

$\frac{3 \cdot (5 x) - 3}{10 x} = 0$

Step 7

Factor $3$ out of $3 \cdot 5 x - 3$ .

Factor $3$ out of $3 \cdot 5 x$ .

$\frac{3 (5 x) - 3}{10 x} = 0$

Factor $3$ out of $- 3$ .

$\frac{3 (5 x) + 3 (- 1)}{10 x} = 0$

Factor $3$ out of $3 (5 x) + 3 (- 1)$ .

$\frac{3 (5 x - 1)}{10 x} = 0$

Step 8

Set the numerator equal to zero.

$3 (5 x - 1) = 0$

Step 9

Solve the equation for $x$ .

Divide each term in $3 (5 x - 1) = 0$ by $3$ and simplify.

Divide each term in $3 (5 x - 1) = 0$ by $3$ .

$\frac{3 (5 x - 1)}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (5 x - 1)}{3} = \frac{0}{3}$

Divide $5 x - 1$ by $1$ .

$5 x - 1 = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$5 x - 1 = 0$

Add $1$ to both sides of the equation.

$5 x = 1$

Divide each term in $5 x = 1$ by $5$ and simplify.

Divide each term in $5 x = 1$ by $5$ .

$\frac{5 x}{5} = \frac{1}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{1}{5}$

Divide $x$ by $1$ .

$x = \frac{1}{5}$

Solve by Factoring 3/2=3/(2x)-6/(5x)

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