SOLUTION: (4u^2 - 1)/(u^3 - 16u) * (u^2 + 4u)/(2u - 1) The answer the book has is (2u + 1) / (u -4) It am a parent and I can't figure this out to explain to my homeschooled child. The

Algebra ->  Expressions-with-variables -> SOLUTION: (4u^2 - 1)/(u^3 - 16u) * (u^2 + 4u)/(2u - 1) The answer the book has is (2u + 1) / (u -4) It am a parent and I can't figure this out to explain to my homeschooled child. The       Log On


   

Question 698436: (4u^2 - 1)/(u^3 - 16u) * (u^2 + 4u)/(2u - 1)
The answer the book has is (2u + 1) / (u -4)
It am a parent and I can't figure this out to explain to my homeschooled child. The chapter is multiplying and dividing rational expressions.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4u^2 - 1

factors to

(2u + 1)(2u - 1)

using the difference of squares rule

The second term "(2u - 1)" cancels with the last term "(2u - 1)" on the very right.

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u^3 - 16u

factors to

u(u^2 - 16)

which further factors to

u(u-4)(u+4)

using the difference of squares rule

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u^2 + 4u

factors to

u(u + 4)

Notice the last two final factorizations have a 'u' and a 'u+4' in common. They cancel

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So after all of the factorizations and cancellations, we go from

(4u^2 - 1)/(u^3 - 16u) * (u^2 + 4u)/(2u - 1)

to

((2u - 1)(2u + 1))/(u(u-4)(u+4)) * (u(u+4))/(2u - 1)

which simplifies to

(2u + 1) / (u-4)