Algebra Examples

$\frac{1}{6 y^{2}} + \frac{- 7}{8 y}$

Step 1

Move the negative in front of the fraction.

$\frac{1}{6 y^{2}} - \frac{7}{8 y}$

Step 2

To write $\frac{1}{6 y^{2}}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{6 y^{2}} \cdot \frac{4}{4} - \frac{7}{8 y}$

Step 3

To write $- \frac{7}{8 y}$ as a fraction with a common denominator, multiply by $\frac{3 y}{3 y}$ .

$\frac{1}{6 y^{2}} \cdot \frac{4}{4} - \frac{7}{8 y} \cdot \frac{3 y}{3 y}$

Step 4

Write each expression with a common denominator of $24 y^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{6 y^{2}}$ by $\frac{4}{4}$ .

$\frac{4}{6 y^{2} \cdot 4} - \frac{7}{8 y} \cdot \frac{3 y}{3 y}$

Step 4.2

Multiply $4$ by $6$ .

$\frac{4}{24 y^{2}} - \frac{7}{8 y} \cdot \frac{3 y}{3 y}$

Step 4.3

Multiply $\frac{7}{8 y}$ by $\frac{3 y}{3 y}$ .

$\frac{4}{24 y^{2}} - \frac{7 (3 y)}{8 y (3 y)}$

Step 4.4

Multiply $3$ by $8$ .

$\frac{4}{24 y^{2}} - \frac{7 (3 y)}{24 y \cdot y}$

Step 4.5

Raise $y$ to the power of $1$ .

$\frac{4}{24 y^{2}} - \frac{7 (3 y)}{24 (y^{1} y)}$

Step 4.6

Raise $y$ to the power of $1$ .

$\frac{4}{24 y^{2}} - \frac{7 (3 y)}{24 (y^{1} y^{1})}$

Step 4.7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4}{24 y^{2}} - \frac{7 (3 y)}{24 y^{1 + 1}}$

Step 4.8

Add $1$ and $1$ .

$\frac{4}{24 y^{2}} - \frac{7 (3 y)}{24 y^{2}}$

Step 5

Combine the numerators over the common denominator.

$\frac{4 - 7 (3 y)}{24 y^{2}}$

Step 6

Multiply $- 7$ by $3$ .

$\frac{4 - 21 y}{24 y^{2}}$