Basic Math Examples

$\frac{y + 3}{3} + \frac{y}{3} = \frac{y - 3}{3}$

Step 1

Multiply both sides by $3$ .

$(\frac{y + 3}{3} + \frac{y}{3}) \cdot 3 = \frac{y - 3}{3} \cdot 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{y + 3}{3} + \frac{y}{3}) \cdot 3$ .

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Step 2.1.1.1

Combine the numerators over the common denominator.

$\frac{y + 3 + y}{3} \cdot 3 = \frac{y - 3}{3} \cdot 3$

Step 2.1.1.2

Add $y$ and $y$ .

$\frac{2 y + 3}{3} \cdot 3 = \frac{y - 3}{3} \cdot 3$

Step 2.1.1.3

Cancel the common factor of $3$ .

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Step 2.1.1.3.1

Cancel the common factor.

$\frac{2 y + 3}{3} \cdot 3 = \frac{y - 3}{3} \cdot 3$

Step 2.1.1.3.2

Rewrite the expression.

$2 y + 3 = \frac{y - 3}{3} \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$2 y + 3 = \frac{y - 3}{3} \cdot 3$

Step 2.2.1.2

Rewrite the expression.

$2 y + 3 = y - 3$

Step 3

Solve for $y$ .

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Step 3.1

Move all terms containing $y$ to the left side of the equation.

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Step 3.1.1

Subtract $y$ from both sides of the equation.

$2 y + 3 - y = - 3$

Step 3.1.2

Subtract $y$ from $2 y$ .

$y + 3 = - 3$

Step 3.2

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

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Step 3.2.1

Subtract $3$ from both sides of the equation.

$y = - 3 - 3$

Step 3.2.2

Subtract $3$ from $- 3$ .

$y = - 6$