Simplify 6/(k-4)+(k+6)/(k^2+2k-24)

$\frac{6}{k - 4} + \frac{k + 6}{k^{2} + 2 k - 24}$

Step 1

Simplify each term.

Factor $k^{2} + 2 k - 24$ 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.

$\frac{6}{k - 4} + \frac{k + 6}{(k - 4) (k + 6)}$

Cancel the common factor of $k + 6$ .

Cancel the common factor.

$\frac{6}{k - 4} + \frac{k + 6}{(k - 4) (k + 6)}$

Rewrite the expression.

$\frac{6}{k - 4} + \frac{1}{k - 4}$

Step 2

Combine fractions.

Combine the numerators over the common denominator.

$\frac{6 + 1}{k - 4}$

Add $6$ and $1$ .

$\frac{7}{k - 4}$

Simplify 6/(k-4)+(k+6)/(k^2+2k-24)

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