Simplify formula: (1/h)((a+h)^2/a+h-1 - a^2/a+1)

[skatru]

It asks to assume a is a constant and h is a variable.

Simplify for f(h)

(1/h)([sup:2o09d81m](a+h)^2[/sup:2o09d81m]/[sub:2o09d81m]a+h-1[/sub:2o09d81m] - [sup:2o09d81m]a^2[/sup:2o09d81m]/[sub:2o09d81m]a+1[/sub:2o09d81m])

I simplified it to (2a+h)/h

but it says the answer is (a^2-2a+ah-h)/(a+h-1)(a-1)

Any help would be appreciated, I'm confused.

 

[tkhunny]

Re: Simplify formula

Unable to decode. Please try again.

 

[soroban]

Re: Simplify formula

Hello, skatru!

There is a typo in the problem . . . I think I've corrected it.

It asks to assume \(\displaystyle a\) is a constant and \(\displaystyle h\) is a variable. . . . . Does this matter?

\(\displaystyle \text{Simplify: }\:\frac{1}{h}\left[\frac{(a+h)^2}{a+h-1} - \frac{a^2}{a-1}\right]\)

\(\displaystyle \text{The answer is: }\; \frac{a^2-2a+ah-h}{(a+h-1)(a-1)}\)

\(\displaystyle \text{Combine the fractions: }\;\frac{1}{h}\left[\frac{(a-1)(a+h)^2 - a^2(a+h-1)}{(a+h-1)(a-1)}\right]\)

. . \(\displaystyle = \;\frac{1}{h}\left[\frac{a^3 + 2a^2h +ah^2 - a^2 - 2ah - h^2 - a^3 - a^2h + a^2}{(a+h-1)(a-1)} \;= \;\frac{a^2h-2ah + ah^2 - h^2}{h(a+h-1)(a-1)}\)

\(\displaystyle \text{Factor: }\;\frac{h(a^2-2a+ah-h)}{h(a+h-1)(a-1)}\)

\(\displaystyle \text{Reduce: }\;\frac{a^2-2a+ah-h}{(a+h-1)(a-1)}\)