Solve for x (3x)/5-(2x)/3+1/5=0

$\frac{3 x}{5} - \frac{2 x}{3} + \frac{1}{5} = 0$

Simplify $\frac{3 x}{5} - \frac{2 x}{3} + \frac{1}{5}$ .

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

$\frac{3 x}{5} \cdot \frac{3}{3} - \frac{2 x}{3} + \frac{1}{5} = 0$

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

$\frac{3 x}{5} \cdot \frac{3}{3} - \frac{2 x}{3} \cdot \frac{5}{5} + \frac{1}{5} = 0$

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{3 x \cdot 3}{5 \cdot 3} - \frac{2 x}{3} \cdot \frac{5}{5} + \frac{1}{5} = 0$

Multiply $5$ by $3$ .

$\frac{3 x \cdot 3}{15} - \frac{2 x}{3} \cdot \frac{5}{5} + \frac{1}{5} = 0$

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

$\frac{3 x \cdot 3}{15} - \frac{2 x \cdot 5}{3 \cdot 5} + \frac{1}{5} = 0$

Multiply $3$ by $5$ .

$\frac{3 x \cdot 3}{15} - \frac{2 x \cdot 5}{15} + \frac{1}{5} = 0$

Combine the numerators over the common denominator.

$\frac{3 x \cdot 3 - 2 x \cdot 5}{15} + \frac{1}{5} = 0$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $3 x \cdot 3 - 2 x \cdot 5$ .

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

$\frac{x (3 \cdot 3) - 2 x \cdot 5}{15} + \frac{1}{5} = 0$

Factor $x$ out of $- 2 x \cdot 5$ .

$\frac{x (3 \cdot 3) + x (- 2 \cdot 5)}{15} + \frac{1}{5} = 0$

Factor $x$ out of $x (3 \cdot 3) + x (- 2 \cdot 5)$ .

$\frac{x (3 \cdot 3 - 2 \cdot 5)}{15} + \frac{1}{5} = 0$

Multiply $3$ by $3$ .

$\frac{x (9 - 2 \cdot 5)}{15} + \frac{1}{5} = 0$

Multiply $- 2$ by $5$ .

$\frac{x (9 - 10)}{15} + \frac{1}{5} = 0$

Subtract $10$ from $9$ .

$\frac{x \cdot - 1}{15} + \frac{1}{5} = 0$

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{15} + \frac{1}{5} = 0$

Move the negative in front of the fraction.

$- \frac{x}{15} + \frac{1}{5} = 0$

Subtract $\frac{1}{5}$ from both sides of the equation.

$- \frac{x}{15} = - \frac{1}{5}$

Multiply both sides of the equation by $- 15$ .

$- 15 (- \frac{x}{15}) = - 15 (- \frac{1}{5})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 15 (- \frac{x}{15})$ .

Cancel the common factor of $15$ .

Move the leading negative in $- \frac{x}{15}$ into the numerator.

$- 15 \frac{- x}{15} = - 15 (- \frac{1}{5})$

Factor $15$ out of $- 15$ .

$15 (- 1) \frac{- x}{15} = - 15 (- \frac{1}{5})$

Cancel the common factor.

$15 \cdot - 1 \frac{- x}{15} = - 15 (- \frac{1}{5})$

Rewrite the expression.

$- - x = - 15 (- \frac{1}{5})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 15 (- \frac{1}{5})$

Multiply $x$ by $1$ .

$x = - 15 (- \frac{1}{5})$

Simplify the right side.

Simplify $- 15 (- \frac{1}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{1}{5}$ into the numerator.

$x = - 15 (\frac{- 1}{5})$

Factor $5$ out of $- 15$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = - 3 \cdot - 1$

Multiply $- 3$ by $- 1$ .

$x = 3$

Solve for x (3x)/5-(2x)/3+1/5=0

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