Algebra Examples

$\frac{5}{2 y} + \frac{1}{6 y} - \frac{4}{3 y}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{5}{2 y}$ by $\frac{3}{3}$ .

$\frac{5}{2 y} \cdot \frac{3}{3} + \frac{1}{6 y} - \frac{4}{3 y}$

Step 1.2

Multiply $\frac{5}{2 y}$ by $\frac{3}{3}$ .

$\frac{5 \cdot 3}{2 y \cdot 3} + \frac{1}{6 y} - \frac{4}{3 y}$

Step 1.3

Multiply $\frac{4}{3 y}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 3}{2 y \cdot 3} + \frac{1}{6 y} - (\frac{4}{3 y} \cdot \frac{2}{2})$

Step 1.4

Multiply $\frac{4}{3 y}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 3}{2 y \cdot 3} + \frac{1}{6 y} - \frac{4 \cdot 2}{3 y \cdot 2}$

Step 1.5

Reorder the factors of $2 y \cdot 3$ .

$\frac{5 \cdot 3}{2 \cdot 3 y} + \frac{1}{6 y} - \frac{4 \cdot 2}{3 y \cdot 2}$

Step 1.6

Multiply $2$ by $3$ .

$\frac{5 \cdot 3}{6 y} + \frac{1}{6 y} - \frac{4 \cdot 2}{3 y \cdot 2}$

Step 1.7

Reorder the factors of $3 y \cdot 2$ .

$\frac{5 \cdot 3}{6 y} + \frac{1}{6 y} - \frac{4 \cdot 2}{2 \cdot 3 y}$

Step 1.8

Multiply $2$ by $3$ .

$\frac{5 \cdot 3}{6 y} + \frac{1}{6 y} - \frac{4 \cdot 2}{6 y}$

Step 2

Combine the numerators over the common denominator.

$\frac{5 \cdot 3 - 4 \cdot 2}{6 y} + \frac{1}{6 y}$

Step 3

Simplify each term.

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Step 3.1

Multiply $5$ by $3$ .

$\frac{15 - 4 \cdot 2}{6 y} + \frac{1}{6 y}$

Step 3.2

Multiply $- 4$ by $2$ .

$\frac{15 - 8}{6 y} + \frac{1}{6 y}$

Step 4

Simplify terms.

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Step 4.1

Subtract $8$ from $15$ .

$\frac{7}{6 y} + \frac{1}{6 y}$

Step 4.2

Combine the numerators over the common denominator.

$\frac{7 + 1}{6 y}$

Step 4.3

Add $7$ and $1$ .

$\frac{8}{6 y}$

Step 4.4

Cancel the common factor of $8$ and $6$ .

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Step 4.4.1

Factor $2$ out of $8$ .

$\frac{2 (4)}{6 y}$

Step 4.4.2

Cancel the common factors.

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Step 4.4.2.1

Factor $2$ out of $6 y$ .

$\frac{2 (4)}{2 (3 y)}$

Step 4.4.2.2

Cancel the common factor.

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

Step 4.4.2.3

Rewrite the expression.

$\frac{4}{3 y}$