Solve the Rational Equation for y y/9-2/5=1/3

$\frac{y}{9} - \frac{2}{5} = \frac{1}{3}$

Step 1

Move all terms not containing $y$ to the right side of the equation.

Add $\frac{2}{5}$ to both sides of the equation.

$\frac{y}{9} = \frac{1}{3} + \frac{2}{5}$

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{y}{9} = \frac{1}{3} \cdot \frac{5}{5} + \frac{2}{5}$

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

$\frac{y}{9} = \frac{1}{3} \cdot \frac{5}{5} + \frac{2}{5} \cdot \frac{3}{3}$

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

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$\frac{y}{9} = \frac{5}{3 \cdot 5} + \frac{2}{5} \cdot \frac{3}{3}$

Multiply $3$ by $5$ .

$\frac{y}{9} = \frac{5}{15} + \frac{2}{5} \cdot \frac{3}{3}$

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

$\frac{y}{9} = \frac{5}{15} + \frac{2 \cdot 3}{5 \cdot 3}$

Multiply $5$ by $3$ .

$\frac{y}{9} = \frac{5}{15} + \frac{2 \cdot 3}{15}$

Combine the numerators over the common denominator.

$\frac{y}{9} = \frac{5 + 2 \cdot 3}{15}$

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{y}{9} = \frac{5 + 6}{15}$

Add $5$ and $6$ .

$\frac{y}{9} = \frac{11}{15}$

Step 2

Multiply both sides of the equation by $9$ .

$9 \frac{y}{9} = 9 (\frac{11}{15})$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$9 \frac{y}{9} = 9 (\frac{11}{15})$

Rewrite the expression.

$y = 9 (\frac{11}{15})$

Simplify the right side.

Simplify $9 (\frac{11}{15})$ .

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$y = 3 (3) \frac{11}{15}$

Factor $3$ out of $15$ .

$y = 3 \cdot 3 \frac{11}{3 \cdot 5}$

Cancel the common factor.

$y = 3 \cdot 3 \frac{11}{3 \cdot 5}$

Rewrite the expression.

$y = 3 (\frac{11}{5})$

Combine $3$ and $\frac{11}{5}$ .

$y = \frac{3 \cdot 11}{5}$

Multiply $3$ by $11$ .

$y = \frac{33}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{33}{5}$

Decimal Form:

$y = 6.6$

Mixed Number Form:

$y = 6 \frac{3}{5}$

Solve the Rational Equation for y y/9-2/5=1/3

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