Simplify (w^2+2w-24)/(w^2+w-30)+8/(w-5)

$\frac{w^{2} + 2 w - 24}{w^{2} + w - 30} + \frac{8}{w - 5}$

Step 1

Simplify each term.

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

$\frac{(w - 4) (w + 6)}{w^{2} + w - 30} + \frac{8}{w - 5}$

Factor $w^{2} + w - 30$ 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 $- 30$ and whose sum is $1$ .

$- 5, 6$

Write the factored form using these integers.

$\frac{(w - 4) (w + 6)}{(w - 5) (w + 6)} + \frac{8}{w - 5}$

Cancel the common factor of $w + 6$ .

Cancel the common factor.

$\frac{(w - 4) (w + 6)}{(w - 5) (w + 6)} + \frac{8}{w - 5}$

Rewrite the expression.

$\frac{w - 4}{w - 5} + \frac{8}{w - 5}$

Step 2

Combine fractions.

Combine the numerators over the common denominator.

$\frac{w - 4 + 8}{w - 5}$

Add $- 4$ and $8$ .

$\frac{w + 4}{w - 5}$

Simplify (w^2+2w-24)/(w^2+w-30)+8/(w-5)

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