Algebra Examples

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

Step 1

Cancel the common factor of $2 x - 4$ and $4$ .

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Step 1.1

Factor $2$ out of $2 x$ .

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

Step 1.2

Factor $2$ out of $- 4$ .

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

Step 1.3

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

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

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $2$ out of $4 x y$ .

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

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

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

Step 2

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

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

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

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

Step 4.5

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

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

Step 4.6

Add $1$ and $1$ .

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

Step 4.7

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

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

Step 4.8

Reorder the factors of $2 x y^{2}$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

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

Step 6.2

Multiply $2$ by $5$ .

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

Step 6.3

Multiply $2$ by $2$ .

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

Step 6.4

Apply the distributive property.

$\frac{10 y + 4 + x y - 2 y}{2 y^{2} x}$

Step 6.5

Subtract $2 y$ from $10 y$ .

$\frac{8 y + 4 + x y}{2 y^{2} x}$