Basic Math Examples

$\frac{- 3}{p^{2} - 8 p} - \frac{5}{p^{3} - 8 p^{2}}$

Step 1

Simplify each term.

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Step 1.1

Factor $p$ out of $p^{2} - 8 p$ .

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Step 1.1.1

Factor $p$ out of $p^{2}$ .

$\frac{- 3}{p \cdot p - 8 p} - \frac{5}{p^{3} - 8 p^{2}}$

Step 1.1.2

Factor $p$ out of $- 8 p$ .

$\frac{- 3}{p \cdot p + p \cdot - 8} - \frac{5}{p^{3} - 8 p^{2}}$

Step 1.1.3

Factor $p$ out of $p \cdot p + p \cdot - 8$ .

$\frac{- 3}{p (p - 8)} - \frac{5}{p^{3} - 8 p^{2}}$

Step 1.2

Move the negative in front of the fraction.

$- \frac{3}{p (p - 8)} - \frac{5}{p^{3} - 8 p^{2}}$

Step 1.3

Factor $p^{2}$ out of $p^{3} - 8 p^{2}$ .

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Step 1.3.1

Factor $p^{2}$ out of $p^{3}$ .

$- \frac{3}{p (p - 8)} - \frac{5}{p^{2} p - 8 p^{2}}$

Step 1.3.2

Factor $p^{2}$ out of $- 8 p^{2}$ .

$- \frac{3}{p (p - 8)} - \frac{5}{p^{2} p + p^{2} \cdot - 8}$

Step 1.3.3

Factor $p^{2}$ out of $p^{2} p + p^{2} \cdot - 8$ .

$- \frac{3}{p (p - 8)} - \frac{5}{p^{2} (p - 8)}$

Step 2

To write $- \frac{3}{p (p - 8)}$ as a fraction with a common denominator, multiply by $\frac{p}{p}$ .

$- \frac{3}{p (p - 8)} \cdot \frac{p}{p} - \frac{5}{p^{2} (p - 8)}$

Step 3

Write each expression with a common denominator of $(p - 8) p^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3}{p (p - 8)}$ by $\frac{p}{p}$ .

$- \frac{3 p}{p (p - 8) p} - \frac{5}{p^{2} (p - 8)}$

Step 3.2

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

$- \frac{3 p}{p^{1} p (p - 8)} - \frac{5}{p^{2} (p - 8)}$

Step 3.3

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

$- \frac{3 p}{p^{1} p^{1} (p - 8)} - \frac{5}{p^{2} (p - 8)}$

Step 3.4

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

$- \frac{3 p}{p^{1 + 1} (p - 8)} - \frac{5}{p^{2} (p - 8)}$

Step 3.5

Add $1$ and $1$ .

$- \frac{3 p}{p^{2} (p - 8)} - \frac{5}{p^{2} (p - 8)}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 3 p - 5}{p^{2} (p - 8)}$

Step 5

Factor $- 1$ out of $- 3 p$ .

$\frac{- (3 p) - 5}{p^{2} (p - 8)}$

Step 6

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

$\frac{- (3 p) - 1 (5)}{p^{2} (p - 8)}$

Step 7

Factor $- 1$ out of $- (3 p) - 1 (5)$ .

$\frac{- (3 p + 5)}{p^{2} (p - 8)}$

Step 8

Simplify the expression.

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Step 8.1

Rewrite $- (3 p + 5)$ as $- 1 (3 p + 5)$ .

$\frac{- 1 (3 p + 5)}{p^{2} (p - 8)}$

Step 8.2

Move the negative in front of the fraction.

$- \frac{3 p + 5}{p^{2} (p - 8)}$