Question

Can someone explain to me how to rewrite a complex rational expression? I am currently trying to use direct substitution on the problem ((1/x-2)+(1/2))/x but I can not for the life of me figure out how to rewrite it. My online class shows me some examples but they are not very good with showing how, what, and why they are doing those steps. Thanks in advance.

Answer 1

\[\frac{\frac{1}{x-2} + \frac{1}{2}}{x}\] is your fraction, right?

The first step I would take is to divide each part of the numerator by the denominator, x. That operation written another way is:
\[\frac{1}{x}*\left(\frac{1}{x-2} + \frac{1}{2}\right) \] Compute that first.

Answer 2

By multiplying the numerator and the denominator by an inverted denominator, the denominator becomes 1 and the fraction is simplified.