Pre-Algebra Examples

$\frac{2 y - 1}{y} + \frac{2 x - 1}{x}$

Step 1

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

$\frac{2 y - 1}{y} \cdot \frac{x}{x} + \frac{2 x - 1}{x}$

Step 2

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

$\frac{2 y - 1}{y} \cdot \frac{x}{x} + \frac{2 x - 1}{x} \cdot \frac{y}{y}$

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

Reorder the factors of $y x$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

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

Step 5.2

Rewrite $- 1 x$ as $- x$ .

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

Step 5.3

Apply the distributive property.

$\frac{2 y x - x + 2 x y - 1 y}{x y}$

Step 5.4

Rewrite $- 1 y$ as $- y$ .

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

Step 5.5

Add $2 y x$ and $2 x y$ .

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Step 5.5.1

Move $y$ .

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

Step 5.5.2

Add $2 x y$ and $2 x y$ .

$\frac{4 x y - x - y}{x y}$