Basic Math Examples

$\frac{5 y}{4 y} + \frac{2 y}{2 y - 1}$

Step 1

Cancel the common factor of $y$ .

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Step 1.1

Cancel the common factor.

$\frac{5 y}{4 y} + \frac{2 y}{2 y - 1}$

Step 1.2

Rewrite the expression.

$\frac{5}{4} + \frac{2 y}{2 y - 1}$

Step 2

To write $\frac{5}{4}$ as a fraction with a common denominator, multiply by $\frac{2 y - 1}{2 y - 1}$ .

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

Step 3

To write $\frac{2 y}{2 y - 1}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 4

Write each expression with a common denominator of $4 (2 y - 1)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5}{4}$ by $\frac{2 y - 1}{2 y - 1}$ .

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

Step 4.2

Multiply $\frac{2 y}{2 y - 1}$ by $\frac{4}{4}$ .

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

Step 4.3

Reorder the factors of $(2 y - 1) \cdot 4$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

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

Step 6.2

Multiply $2$ by $5$ .

$\frac{10 y + 5 \cdot - 1 + 2 y \cdot 4}{4 (2 y - 1)}$

Step 6.3

Multiply $5$ by $- 1$ .

$\frac{10 y - 5 + 2 y \cdot 4}{4 (2 y - 1)}$

Step 6.4

Multiply $4$ by $2$ .

$\frac{10 y - 5 + 8 y}{4 (2 y - 1)}$

Step 6.5

Add $10 y$ and $8 y$ .

$\frac{18 y - 5}{4 (2 y - 1)}$