Simple algebra simplification question? Hello everyone I have the following question.
I have the following fraction
$f(x)=-\frac{4}{x^2}+\frac{1}{(x-1)^2}$
But how would I reduce it I know I have to use the multiply the opposite numerator by denominator and I got.
$(x-1)^2(4)=4x^2-8x+4$
$1(x^2)=x^2$
So I got got $f(x)=-\frac{4x^2-8x+4+x^2}{x^2(x-1)^2}$
But this is incorrect.What am I doing wrong.

You are close.
Your mistake was applying the "-"
to both terms instead of just one.
You wrote
$f(x)=-\frac{4x^2-8x+4+x^2}{x(x-1)^2}$.
What you should have is
$f(x)=\frac{-(4x^2-8x+4)+x^2}{x(x-1)^2}
=\frac{-4x^2+8x-4+x^2}{x(x-1)^2}
=\frac{-3x^2+8x-4}{x(x-1)^2}
$.
