Algebraic expressions: Nested fractions problem

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humperderp

2020. március 28. 14:58

I am posting the same issue Jimbobsjourney had here: https://khanacademy.zendesk.com/hc/en-us/community/posts/360039476211-Nested-Fractions, as he never got a response. I am struggling with the question where 2 + 2/x / 4 - 4/x is supposed to equate to x + 1 / 2(x + 1). I can follow the explanation until step 4/5, as included below, where it just skips the explanation of how you get from x(2x+2)/x(4x-4) to 2x(x+1)/4x(x-1). Where do the 1s come from that replace both -4 and 2?

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Ronen A

2020. március 29. 4:58
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They come from factoring out a two from both numerator and denominator.
humperderp

2020. március 29. 14:15
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Thanks for your reply, and apologies if I'm just being slow here, but if you factor out 2 from x(4x - 4) wouldn't that equate to 2x(2x - 2)?
Ronen A

2020. március 29. 23:15
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yeah my bad - you factor out a two from the top expression and a 4 from the bottom expression.

Then once you do that you simplify the entire fraction
humperderp

2020. március 30. 13:23
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Doi! I was just stuck in the mindset that you have to treat the numerator and denominator equally when canceling out - that doesn't apply when factoring out of the expressions of course. Thank you very much.

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Algebraic expressions: Nested fractions problem

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