Pre-Algebra Examples

$\frac{- 3}{y - 4} - \frac{7}{4 - y}$

Step 1

Move the negative in front of the fraction.

$- \frac{3}{y - 4} - \frac{7}{4 - y}$

Step 2

Rewrite $4$ as $- 1 (- 4)$ .

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

Step 3

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

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

Step 4

Factor $- 1$ out of $- 1 (- 4) - (y)$ .

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

Step 5

Reorder terms.

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

Step 6

To write $- \frac{3}{y - 4}$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

$- \frac{3}{y - 4} \cdot \frac{- 1}{- 1} - \frac{7}{- 1 (y - 4)}$

Step 7

Write each expression with a common denominator of $(y - 4) \cdot - 1$ , by multiplying each by an appropriate factor of $1$ .

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Step 7.1

Multiply $\frac{3}{y - 4}$ by $\frac{- 1}{- 1}$ .

$- \frac{3 \cdot - 1}{(y - 4) \cdot - 1} - \frac{7}{- 1 (y - 4)}$

Step 7.2

Reorder the factors of $(y - 4) \cdot - 1$ .

$- \frac{3 \cdot - 1}{- (y - 4)} - \frac{7}{- 1 (y - 4)}$

Step 8

Combine the numerators over the common denominator.

$\frac{- 3 \cdot - 1 - 7}{- (y - 4)}$

Step 9

Simplify the numerator.

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Step 9.1

Multiply $- 3$ by $- 1$ .

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

Step 9.2

Subtract $7$ from $3$ .

$\frac{- 4}{- (y - 4)}$

Step 10

Dividing two negative values results in a positive value.

$\frac{4}{y - 4}$