Algebra Examples

$\frac{2 x}{y^{2}} + \frac{3 x}{2 y} - \frac{4 x}{5}$

Step 1

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

$\frac{2 x}{y^{2}} \cdot \frac{2}{2} + \frac{3 x}{2 y} - \frac{4 x}{5}$

Step 2

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

$\frac{2 x}{y^{2}} \cdot \frac{2}{2} + \frac{3 x}{2 y} \cdot \frac{y}{y} - \frac{4 x}{5}$

Step 3

Write each expression with a common denominator of $2 y^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$\frac{2 x \cdot 2}{y^{2} \cdot 2} + \frac{3 x}{2 y} \cdot \frac{y}{y} - \frac{4 x}{5}$

Step 3.2

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

$\frac{2 x \cdot 2}{y^{2} \cdot 2} + \frac{3 x y}{2 y \cdot y} - \frac{4 x}{5}$

Step 3.3

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

$\frac{2 x \cdot 2}{y^{2} \cdot 2} + \frac{3 x y}{2 (y^{1} y)} - \frac{4 x}{5}$

Step 3.4

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

$\frac{2 x \cdot 2}{y^{2} \cdot 2} + \frac{3 x y}{2 (y^{1} y^{1})} - \frac{4 x}{5}$

Step 3.5

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

$\frac{2 x \cdot 2}{y^{2} \cdot 2} + \frac{3 x y}{2 y^{1 + 1}} - \frac{4 x}{5}$

Step 3.6

Add $1$ and $1$ .

$\frac{2 x \cdot 2}{y^{2} \cdot 2} + \frac{3 x y}{2 y^{2}} - \frac{4 x}{5}$

Step 3.7

Reorder the factors of $y^{2} \cdot 2$ .

$\frac{2 x \cdot 2}{2 y^{2}} + \frac{3 x y}{2 y^{2}} - \frac{4 x}{5}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 x \cdot 2 + 3 x y}{2 y^{2}} - \frac{4 x}{5}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $x$ out of $2 x \cdot 2 + 3 x y$ .

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Step 5.1.1

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

$\frac{x (2 \cdot 2) + 3 x y}{2 y^{2}} - \frac{4 x}{5}$

Step 5.1.2

Factor $x$ out of $3 x y$ .

$\frac{x (2 \cdot 2) + x (3 y)}{2 y^{2}} - \frac{4 x}{5}$

Step 5.1.3

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

$\frac{x (2 \cdot 2 + 3 y)}{2 y^{2}} - \frac{4 x}{5}$

Step 5.2

Multiply $2$ by $2$ .

$\frac{x (4 + 3 y)}{2 y^{2}} - \frac{4 x}{5}$

Step 6

To write $\frac{x (4 + 3 y)}{2 y^{2}}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x (4 + 3 y)}{2 y^{2}} \cdot \frac{5}{5} - \frac{4 x}{5}$

Step 7

To write $- \frac{4 x}{5}$ as a fraction with a common denominator, multiply by $\frac{2 y^{2}}{2 y^{2}}$ .

$\frac{x (4 + 3 y)}{2 y^{2}} \cdot \frac{5}{5} - \frac{4 x}{5} \cdot \frac{2 y^{2}}{2 y^{2}}$

Step 8

Write each expression with a common denominator of $10 y^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 8.1

Multiply $\frac{x (4 + 3 y)}{2 y^{2}}$ by $\frac{5}{5}$ .

$\frac{x (4 + 3 y) \cdot 5}{2 y^{2} \cdot 5} - \frac{4 x}{5} \cdot \frac{2 y^{2}}{2 y^{2}}$

Step 8.2

Multiply $5$ by $2$ .

$\frac{x (4 + 3 y) \cdot 5}{10 y^{2}} - \frac{4 x}{5} \cdot \frac{2 y^{2}}{2 y^{2}}$

Step 8.3

Multiply $\frac{4 x}{5}$ by $\frac{2 y^{2}}{2 y^{2}}$ .

$\frac{x (4 + 3 y) \cdot 5}{10 y^{2}} - \frac{4 x (2 y^{2})}{5 (2 y^{2})}$

Step 8.4

Multiply $2$ by $5$ .

$\frac{x (4 + 3 y) \cdot 5}{10 y^{2}} - \frac{4 x (2 y^{2})}{10 y^{2}}$

Step 9

Combine the numerators over the common denominator.

$\frac{x (4 + 3 y) \cdot 5 - 4 x (2 y^{2})}{10 y^{2}}$

Step 10

Simplify the numerator.

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Step 10.1

Factor $x$ out of $x (4 + 3 y) \cdot 5 - 4 x \cdot 2 y^{2}$ .

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Step 10.1.1

Factor $x$ out of $x (4 + 3 y) \cdot 5$ .

$\frac{x ((4 + 3 y) \cdot 5) - 4 x \cdot 2 y^{2}}{10 y^{2}}$

Step 10.1.2

Factor $x$ out of $- 4 x \cdot 2 y^{2}$ .

$\frac{x ((4 + 3 y) \cdot 5) + x (- 4 \cdot 2 y^{2})}{10 y^{2}}$

Step 10.1.3

Factor $x$ out of $x ((4 + 3 y) \cdot 5) + x (- 4 \cdot 2 y^{2})$ .

$\frac{x ((4 + 3 y) \cdot 5 - 4 \cdot 2 y^{2})}{10 y^{2}}$

Step 10.2

Apply the distributive property.

$\frac{x (4 \cdot 5 + 3 y \cdot 5 - 4 \cdot 2 y^{2})}{10 y^{2}}$

Step 10.3

Multiply $4$ by $5$ .

$\frac{x (20 + 3 y \cdot 5 - 4 \cdot 2 y^{2})}{10 y^{2}}$

Step 10.4

Multiply $5$ by $3$ .

$\frac{x (20 + 15 y - 4 \cdot 2 y^{2})}{10 y^{2}}$

Step 10.5

Multiply $- 4$ by $2$ .

$\frac{x (20 + 15 y - 8 y^{2})}{10 y^{2}}$