Pre-Algebra Examples

$\frac{5}{2 p - 5} + \frac{7}{5 - 2 p}$

Step 1

Rewrite $5$ as $- 1 (- 5)$ .

$\frac{5}{2 p - 5} + \frac{7}{- 1 (- 5) - 2 p}$

Step 2

Factor $- 1$ out of $- 2 p$ .

$\frac{5}{2 p - 5} + \frac{7}{- 1 (- 5) - (2 p)}$

Step 3

Factor $- 1$ out of $- 1 (- 5) - (2 p)$ .

$\frac{5}{2 p - 5} + \frac{7}{- 1 (- 5 + 2 p)}$

Step 4

Simplify the expression.

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Step 4.1

Move a negative from the denominator of $\frac{7}{- 1 (- 5 + 2 p)}$ to the numerator.

$\frac{5}{2 p - 5} + \frac{- 1 \cdot 7}{- 5 + 2 p}$

Step 4.2

Reorder terms.

$\frac{5}{2 p - 5} + \frac{- 1 \cdot 7}{2 p - 5}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 - 1 \cdot 7}{2 p - 5}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 1$ by $7$ .

$\frac{5 - 7}{2 p - 5}$

Step 6.2

Subtract $7$ from $5$ .

$\frac{- 2}{2 p - 5}$

Step 7

Move the negative in front of the fraction.

$- \frac{2}{2 p - 5}$