Basic Math Examples

$\frac{5 r + 15}{r^{2} - 5 r - 24} - \frac{6}{r - 8}$

Step 1

Simplify each term.

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Step 1.1

Factor $5$ out of $5 r + 15$ .

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Step 1.1.1

Factor $5$ out of $5 r$ .

$\frac{5 (r) + 15}{r^{2} - 5 r - 24} - \frac{6}{r - 8}$

Step 1.1.2

Factor $5$ out of $15$ .

$\frac{5 r + 5 \cdot 3}{r^{2} - 5 r - 24} - \frac{6}{r - 8}$

Step 1.1.3

Factor $5$ out of $5 r + 5 \cdot 3$ .

$\frac{5 (r + 3)}{r^{2} - 5 r - 24} - \frac{6}{r - 8}$

Step 1.2

Factor $r^{2} - 5 r - 24$ using the AC method.

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Step 1.2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 24$ and whose sum is $- 5$ .

$- 8, 3$

Step 1.2.2

Write the factored form using these integers.

$\frac{5 (r + 3)}{(r - 8) (r + 3)} - \frac{6}{r - 8}$

Step 1.3

Cancel the common factor of $r + 3$ .

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Step 1.3.1

Cancel the common factor.

$\frac{5 (r + 3)}{(r - 8) (r + 3)} - \frac{6}{r - 8}$

Step 1.3.2

Rewrite the expression.

$\frac{5}{r - 8} - \frac{6}{r - 8}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{5 - 6}{r - 8}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract $6$ from $5$ .

$\frac{- 1}{r - 8}$

Step 2.2.2

Move the negative in front of the fraction.

$- \frac{1}{r - 8}$