Solving algebra equation with fractions...

[Guest]

How is this equation ;

f(x) = 1 / (x2-4)
g(x) = 2x+1

h(x) = g(f(x))

Hence...
2(1 / (x2-4)) + 1

I cant figure out how the answer can come to (x2 - 2) / (x2 - 4)
Any help is very appreciated. Thanks in advance.

 

[soroban]

Hello, avae_090!

\(\displaystyle f(x)\:=\:\frac{1}{x^2-4},\;\;\;g(x)\:=\:2x\,+\,1\)

Find: .\(\displaystyle h(x)\:=\:g(f(x))\)

Hence . . . \(\displaystyle 2\left(\frac{1}{x^2-4}\right)\,+\,1\) . . . . correct!

I cant figure out how the answer can come to \(\displaystyle \L\frac{x^2 - 2}{x^2 - 4}\)

Get a common denominator and add the fractions . . .

We have: .\(\displaystyle \L\frac{2}{x^2\,-\,4}\,+\,1\;=\;\frac{2}{x^2\,-\,4}\,+\,\frac{x^2\,-\,4}{x^2\,-\,4}\;=\;\frac{2\,+\,x^2\,-\,4}{x^2\,-\,4}\;=\;\frac{x^2\,-\,2}{x^2\,-\,4}\)