Algebra Examples

$\frac{\frac{4}{2 y} - \frac{1}{2 y}}{\frac{4}{2 y} + \frac{3}{y}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

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

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Step 1.1.1

Factor $2$ out of $4$ .

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

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $2 y$ .

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

Step 1.1.2.2

Cancel the common factor.

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

Step 1.1.2.3

Rewrite the expression.

$\frac{\frac{2}{y} - \frac{1}{2 y}}{\frac{4}{2 y} + \frac{3}{y}}$

Step 1.2

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

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Step 1.2.1

Factor $2$ out of $4$ .

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

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $2$ out of $2 y$ .

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

Step 1.2.2.2

Cancel the common factor.

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

Step 1.2.2.3

Rewrite the expression.

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

Step 2

Multiply the numerator and denominator of the fraction by $y \cdot 2$ .

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Step 2.1

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

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

Step 2.2

Combine.

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

Step 3

Apply the distributive property.

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

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

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

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

Step 4.1.2

Cancel the common factor.

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

Step 4.1.3

Rewrite the expression.

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

Step 4.2

Multiply $2$ by $2$ .

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

Step 4.3

Cancel the common factor of $2 y$ .

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Step 4.3.1

Move the leading negative in $- \frac{1}{2 y}$ into the numerator.

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

Step 4.3.2

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

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

Step 4.3.3

Cancel the common factor.

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

Step 4.3.4

Rewrite the expression.

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

Step 4.4

Cancel the common factor of $y$ .

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Step 4.4.1

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

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

Step 4.4.2

Cancel the common factor.

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

Step 4.4.3

Rewrite the expression.

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

Step 4.5

Multiply $2$ by $2$ .

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

Step 4.6

Cancel the common factor of $y$ .

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Step 4.6.1

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

$\frac{4 - 1}{4 + y (2) \frac{3}{y}}$

Step 4.6.2

Cancel the common factor.

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

Step 4.6.3

Rewrite the expression.

$\frac{4 - 1}{4 + 2 \cdot 3}$

Step 4.7

Multiply $2$ by $3$ .

$\frac{4 - 1}{4 + 6}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Subtract $1$ from $4$ .

$\frac{3}{4 + 6}$

Step 5.2

Add $4$ and $6$ .

$\frac{3}{10}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{10}$

Decimal Form:

$0.3$