Simplify 5/(x+6)-3/(x^2+2x-24)

$\frac{5}{x + 6} - \frac{3}{x^{2} + 2 x - 24}$

Factor $x^{2} + 2 x - 24$ using the AC method.

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 $2$ .

$- 4, 6$

Write the factored form using these integers.

$\frac{5}{x + 6} - \frac{3}{(x - 4) (x + 6)}$

To write $\frac{5}{x + 6}$ as a fraction with a common denominator, multiply by $\frac{x - 4}{x - 4}$ .

$\frac{5}{x + 6} \cdot \frac{x - 4}{x - 4} - \frac{3}{(x - 4) (x + 6)}$

Write each expression with a common denominator of $(x + 6) (x - 4)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{x + 6}$ by $\frac{x - 4}{x - 4}$ .

$\frac{5 (x - 4)}{(x + 6) (x - 4)} - \frac{3}{(x - 4) (x + 6)}$

Reorder the factors of $(x - 4) (x + 6)$ .

$\frac{5 (x - 4)}{(x + 6) (x - 4)} - \frac{3}{(x + 6) (x - 4)}$

Combine the numerators over the common denominator.

$\frac{5 (x - 4) - 3}{(x + 6) (x - 4)}$

Simplify the numerator.

Apply the distributive property.

$\frac{5 x + 5 \cdot - 4 - 3}{(x + 6) (x - 4)}$

Multiply $5$ by $- 4$ .

$\frac{5 x - 20 - 3}{(x + 6) (x - 4)}$

Subtract $3$ from $- 20$ .

$\frac{5 x - 23}{(x + 6) (x - 4)}$

Simplify 5/(x+6)-3/(x^2+2x-24)

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