Basic Math Examples

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

Step 1

Factor $5$ out of $5 p + 5$ .

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Step 1.1

Factor $5$ out of $5 p$ .

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

Step 1.2

Factor $5$ out of $5$ .

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

Step 1.3

Factor $5$ out of $5 (p) + 5 (1)$ .

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

Step 2

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

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

Step 3

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

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

Step 4

Factor $- 1$ out of $- 1 (- 7) - (p)$ .

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

Step 5

Reorder terms.

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

Step 6

To write $\frac{5 p^{2} - 1}{p - 7}$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

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

Step 7

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

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Step 7.1

Multiply $\frac{5 p^{2} - 1}{p - 7}$ by $\frac{- 1}{- 1}$ .

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

Step 7.2

Reorder the factors of $(p - 7) \cdot - 1$ .

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

Step 8

Combine the numerators over the common denominator.

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

Step 9

Simplify the numerator.

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Step 9.1

Apply the distributive property.

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

Step 9.2

Multiply $- 1$ by $5$ .

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

Step 9.3

Multiply $- 1$ by $- 1$ .

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

Step 9.4

Apply the distributive property.

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

Step 9.5

Multiply $- 5$ by $1$ .

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

Step 9.6

Subtract $5$ from $1$ .

$\frac{- 5 p^{2} - 5 p - 4}{- (p - 7)}$

Step 10

Simplify with factoring out.

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Step 10.1

Move the negative in front of the fraction.

$- \frac{- 5 p^{2} - 5 p - 4}{p - 7}$

Step 10.2

Factor $- 1$ out of $- 5 p^{2}$ .

$- \frac{- (5 p^{2}) - 5 p - 4}{p - 7}$

Step 10.3

Factor $- 1$ out of $- 5 p$ .

$- \frac{- (5 p^{2}) - (5 p) - 4}{p - 7}$

Step 10.4

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

$- \frac{- (5 p^{2} + 5 p) - 4}{p - 7}$

Step 10.5

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

$- \frac{- (5 p^{2} + 5 p) - 1 (4)}{p - 7}$

Step 10.6

Factor $- 1$ out of $- (5 p^{2} + 5 p) - 1 (4)$ .

$- \frac{- (5 p^{2} + 5 p + 4)}{p - 7}$

Step 10.7

Simplify the expression.

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Step 10.7.1

Rewrite $- (5 p^{2} + 5 p + 4)$ as $- 1 (5 p^{2} + 5 p + 4)$ .

$- \frac{- 1 (5 p^{2} + 5 p + 4)}{p - 7}$

Step 10.7.2

Move the negative in front of the fraction.

$- - \frac{5 p^{2} + 5 p + 4}{p - 7}$

Step 10.7.3

Multiply $- 1$ by $- 1$ .

$1 \frac{5 p^{2} + 5 p + 4}{p - 7}$

Step 10.7.4

Multiply $\frac{5 p^{2} + 5 p + 4}{p - 7}$ by $1$ .

$\frac{5 p^{2} + 5 p + 4}{p - 7}$