Simplify 12/(x^2+5x-24)+3/(x-3)

$\frac{12}{x^{2} + 5 x - 24} + \frac{3}{x - 3}$

Factor $x^{2} + 5 x - 24$ 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 $5$ .

$- 3, 8$

Write the factored form using these integers.

$\frac{12}{(x - 3) (x + 8)} + \frac{3}{x - 3}$

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

$\frac{12}{(x - 3) (x + 8)} + \frac{3}{x - 3} \cdot \frac{x + 8}{x + 8}$

Simplify terms.

Multiply $\frac{3}{x - 3}$ by $\frac{x + 8}{x + 8}$ .

$\frac{12}{(x - 3) (x + 8)} + \frac{3 (x + 8)}{(x - 3) (x + 8)}$

Combine the numerators over the common denominator.

$\frac{12 + 3 (x + 8)}{(x - 3) (x + 8)}$

Simplify the numerator.

Factor $3$ out of $12 + 3 (x + 8)$ .

Factor $3$ out of $12$ .

$\frac{3 \cdot 4 + 3 (x + 8)}{(x - 3) (x + 8)}$

Factor $3$ out of $3 \cdot 4 + 3 (x + 8)$ .

$\frac{3 (4 + x + 8)}{(x - 3) (x + 8)}$

Add $4$ and $8$ .

$\frac{3 (x + 12)}{(x - 3) (x + 8)}$

Simplify 12/(x^2+5x-24)+3/(x-3)

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