Finite Math Examples

$\frac{3 x}{2 y} + \frac{2 x - y^{2}}{3}$

Step 1

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

$\frac{3 x}{2 y} \cdot \frac{3}{3} + \frac{2 x - y^{2}}{3}$

Step 2

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

$\frac{3 x}{2 y} \cdot \frac{3}{3} + \frac{2 x - y^{2}}{3} \cdot \frac{2 y}{2 y}$

Step 3

Write each expression with a common denominator of $6 y$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$\frac{3 x \cdot 3}{2 y \cdot 3} + \frac{2 x - y^{2}}{3} \cdot \frac{2 y}{2 y}$

Step 3.2

Multiply $3$ by $2$ .

$\frac{3 x \cdot 3}{6 y} + \frac{2 x - y^{2}}{3} \cdot \frac{2 y}{2 y}$

Step 3.3

Multiply $\frac{2 x - y^{2}}{3}$ by $\frac{2 y}{2 y}$ .

$\frac{3 x \cdot 3}{6 y} + \frac{(2 x - y^{2}) (2 y)}{3 (2 y)}$

Step 3.4

Multiply $2$ by $3$ .

$\frac{3 x \cdot 3}{6 y} + \frac{(2 x - y^{2}) (2 y)}{6 y}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 x \cdot 3 + (2 x - y^{2}) (2 y)}{6 y}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $3$ .

$\frac{9 x + (2 x - y^{2}) \cdot 2 y}{6 y}$

Step 5.2

Apply the distributive property.

$\frac{9 x + (2 x \cdot 2 - y^{2} \cdot 2) y}{6 y}$

Step 5.3

Multiply $2$ by $2$ .

$\frac{9 x + (4 x - y^{2} \cdot 2) y}{6 y}$

Step 5.4

Multiply $2$ by $- 1$ .

$\frac{9 x + (4 x - 2 y^{2}) y}{6 y}$

Step 5.5

Apply the distributive property.

$\frac{9 x + 4 x y - 2 y^{2} y}{6 y}$

Step 5.6

Multiply $y^{2}$ by $y$ by adding the exponents.

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Step 5.6.1

Move $y$ .

$\frac{9 x + 4 x y - 2 (y \cdot y^{2})}{6 y}$

Step 5.6.2

Multiply $y$ by $y^{2}$ .

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Step 5.6.2.1

Raise $y$ to the power of $1$ .

$\frac{9 x + 4 x y - 2 (y^{1} y^{2})}{6 y}$

Step 5.6.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{9 x + 4 x y - 2 y^{1 + 2}}{6 y}$

Step 5.6.3

Add $1$ and $2$ .

$\frac{9 x + 4 x y - 2 y^{3}}{6 y}$