Simplify (3u^2+12u-96)/(u^2+12u+32u)

Math
3u2+12u-96u2+12u+32u
Simplify the numerator.
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Factor 3 out of 3u2+12u-96.
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Factor 3 out of 3u2.
3(u2)+12u-96u2+12u+32u
Factor 3 out of 12u.
3(u2)+3(4u)-96u2+12u+32u
Factor 3 out of -96.
3u2+3(4u)+3⋅-32u2+12u+32u
Factor 3 out of 3u2+3(4u).
3(u2+4u)+3⋅-32u2+12u+32u
Factor 3 out of 3(u2+4u)+3⋅-32.
3(u2+4u-32)u2+12u+32u
3(u2+4u-32)u2+12u+32u
Factor u2+4u-32 using the AC method.
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Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -32 and whose sum is 4.
-4,8
Write the factored form using these integers.
3((u-4)(u+8))u2+12u+32u
3(u-4)(u+8)u2+12u+32u
3(u-4)(u+8)u2+12u+32u
Simplify the denominator.
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Add 12u and 32u.
3(u-4)(u+8)u2+44u
Factor u out of u2+44u.
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Factor u out of u2.
3(u-4)(u+8)u⋅u+44u
Factor u out of 44u.
3(u-4)(u+8)u⋅u+u⋅44
Factor u out of u⋅u+u⋅44.
3(u-4)(u+8)u(u+44)
3(u-4)(u+8)u(u+44)
3(u-4)(u+8)u(u+44)
Simplify (3u^2+12u-96)/(u^2+12u+32u)

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