Simplify p/(7a-14)+1/(2-a)

$\frac{p}{7 a - 14} + \frac{1}{2 - a}$

Step 1

Factor $7$ out of $7 a - 14$ .

Factor $7$ out of $7 a$ .

$\frac{p}{7 (a) - 14} + \frac{1}{2 - a}$

Factor $7$ out of $- 14$ .

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

Factor $7$ out of $7 a + 7 \cdot - 2$ .

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

Step 2

Rewrite $2$ as $- 1 (- 2)$ .

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

Step 3

Factor $- 1$ out of $- a$ .

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

Step 4

Factor $- 1$ out of $- 1 (- 2) - (a)$ .

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

Step 5

Simplify the expression.

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

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

Reorder terms.

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

Step 6

To write $\frac{- 1 \cdot 1}{a - 2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

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

Step 7

Write each expression with a common denominator of $7 (a - 2)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{- 1 \cdot 1}{a - 2}$ by $\frac{7}{7}$ .

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

Reorder the factors of $(a - 2) \cdot 7$ .

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

Step 8

Combine the numerators over the common denominator.

$\frac{p - 1 \cdot 7}{7 (a - 2)}$

Step 9

Multiply $- 1$ by $7$ .

$\frac{p - 7}{7 (a - 2)}$