Pre-Algebra Examples

$\frac{- 5}{2 y} - \frac{7}{6 y^{2}}$

Step 1

Move the negative in front of the fraction.

$- \frac{5}{2 y} - \frac{7}{6 y^{2}}$

Step 2

To write $- \frac{5}{2 y}$ as a fraction with a common denominator, multiply by $\frac{3 y}{3 y}$ .

$- \frac{5}{2 y} \cdot \frac{3 y}{3 y} - \frac{7}{6 y^{2}}$

Step 3

Write each expression with a common denominator of $6 y^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$- \frac{5 (3 y)}{2 y (3 y)} - \frac{7}{6 y^{2}}$

Step 3.2

Multiply $3$ by $2$ .

$- \frac{5 (3 y)}{6 y \cdot y} - \frac{7}{6 y^{2}}$

Step 3.3

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

$- \frac{5 (3 y)}{6 (y^{1} y)} - \frac{7}{6 y^{2}}$

Step 3.4

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

$- \frac{5 (3 y)}{6 (y^{1} y^{1})} - \frac{7}{6 y^{2}}$

Step 3.5

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

$- \frac{5 (3 y)}{6 y^{1 + 1}} - \frac{7}{6 y^{2}}$

Step 3.6

Add $1$ and $1$ .

$- \frac{5 (3 y)}{6 y^{2}} - \frac{7}{6 y^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 5 (3 y) - 7}{6 y^{2}}$

Step 5

Multiply $- 5$ by $3$ .

$\frac{- 15 y - 7}{6 y^{2}}$

Step 6

Factor $- 1$ out of $- 15 y$ .

$\frac{- (15 y) - 7}{6 y^{2}}$

Step 7

Rewrite $- 7$ as $- 1 (7)$ .

$\frac{- (15 y) - 1 (7)}{6 y^{2}}$

Step 8

Factor $- 1$ out of $- (15 y) - 1 (7)$ .

$\frac{- (15 y + 7)}{6 y^{2}}$

Step 9

Simplify the expression.

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Step 9.1

Rewrite $- (15 y + 7)$ as $- 1 (15 y + 7)$ .

$\frac{- 1 (15 y + 7)}{6 y^{2}}$

Step 9.2

Move the negative in front of the fraction.

$- \frac{15 y + 7}{6 y^{2}}$