Algebra Examples

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

Step 1

Cancel the common factor of $x$ .

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Step 1.1

Cancel the common factor.

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

Step 1.2

Rewrite the expression.

$\frac{\frac{1}{y} - 2}{2 x y - \frac{3}{y}}$

Step 2

Multiply the numerator and denominator of the fraction by $y$ .

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Step 2.1

Multiply $\frac{\frac{1}{y} - 2}{2 x y - \frac{3}{y}}$ by $\frac{y}{y}$ .

$\frac{y}{y} \cdot \frac{\frac{1}{y} - 2}{2 x y - \frac{3}{y}}$

Step 2.2

Combine.

$\frac{y (\frac{1}{y} - 2)}{y (2 x y - \frac{3}{y})}$

Step 3

Apply the distributive property.

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

Step 4

Simplify by cancelling.

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Step 4.1

Cancel the common factor of $y$ .

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Step 4.1.1

Cancel the common factor.

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

Step 4.1.2

Rewrite the expression.

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

Step 4.2

Cancel the common factor of $y$ .

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Step 4.2.1

Move the leading negative in $- \frac{3}{y}$ into the numerator.

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Move $- 2$ to the left of $y$ .

$\frac{1 - 2 y}{y (2 x y) - 3}$

Step 6

Simplify the denominator.

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Step 6.1

Rewrite using the commutative property of multiplication.

$\frac{1 - 2 y}{2 y (x y) - 3}$

Step 6.2

Multiply $y$ by $y$ by adding the exponents.

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Step 6.2.1

Move $y$ .

$\frac{1 - 2 y}{2 (y \cdot y) x - 3}$

Step 6.2.2

Multiply $y$ by $y$ .

$\frac{1 - 2 y}{2 y^{2} x - 3}$