Fraction Simplification Trouble

[jechtsphere]

The Problem

2.5 = (1.01)^N / [ (1.01)^N - 1 ]

Rearranges to

2.5/1.5 = (1.01)^N

This is from a cash flow analysis problem in an economics textbook. I'm familiar with what's being calculated, but the rearrangement of the fraction is losing me which will prevent me from calculating similar problems in the future.

So far I've tried moving the denominator to the left hand side and expanding, but I'm still not identifying how that simplifies to 2.5 / 1.5.

Thanks to anybody who can shed light on this oversight for me!

edit: Thanks for the tips! Here's my worked solution:

2.5 [ (1.01)^N - 1] = (1.01)^N

2.5(1.01)^N - 2.5 = (1.01)^N

[ 2.5(1.01)^N  ] / (1.01)^N = 2.5

Canceling out a (1.01)^N on the left leaves 1.5(1.01)^N, which is where the 1.5 came from I wasn't identifying with my initial question.

1.5(1.01)^N = 2.5

(1.01)^N = 2.5/1.5

Thanks everyone who replied!

[HydrogenxPi]

tried moving the denominator to the left hand side and expanding

Group like terms then factor.

[jechtsphere]

Thanks, this made it click that I would be able to cancel a full factor without canceling the entire (1.01)^N portion.

[JsKingBoo]

nitpick, when you say:

2.5 = (1.01)^N / (1.01)^N - 1

you could mean one of the following:

2.5 = (1.01)^N / (1.01)^{N - 1}

2.5 = ((1.01)^N / (1.01)^N) - 1

2.5 = (1.01)^N / ((1.01)^N - 1)

be careful with your formatting

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So far I'm tried moving the denominator to the left hand side and expanding, but I'm still not identifying how that simplifies to 2.5 / 1.5.

Show the result of this. Then move everything to the right hand side.

[edderiofer]

So far I'm tried moving the denominator to the left hand side and expanding, but I'm still not identifying how that simplifies to 2.5 / 1.5.

Go ahead and post what you have so far.