Question

How would I go about simplifying this equation?

Answer 1

\[\frac{ 2 }{ x ^{2} - x } - \frac{ 1 }{ x }\]

Answer 2

I know I have to factor/find a common denominator, but I'm having difficulty.

Answer 3

The denominators actually have a common factor.
It's difficult to see it at first though.

Let's factor this expression to start, \(\large\rm x^2-x\)
Each term shares something in common, see it? :)

Answer 4

The x's, right?

Answer 5

Mmm good, they both have an x.
If we pull that out of each term,\[\large\rm x(x-1)\]

Answer 6

Any confusion on that first factoring step? :o\[\large\rm \frac{2}{x(x-1)}-\frac{1}{x}\]
After that, you'll notice that they share the x denominator, ya?

Answer 7

No confusion there, I can follow that easily enough. :) And yes, I see they share the x-denominator.

Answer 8

So I guess we have to give our second fraction this (x-1) in order to get a common denominator. Giving to both the numerator and denominator.\[\large\rm \frac{2}{x(x-1)}-\frac{1}{x}\cdot\color{royalblue}{\frac{(x-1)}{(x-1)}}\]

Answer 9

Ohh, okay! That makes sense. So from there I just combine the rational expressions and simplify, right?

Answer 10

Good, yes.
You can combine it into a single fraction,\[\large\rm \frac{2-1(x-1)}{x(x-1)}\]and simplify.

Answer 11

\[\frac{ x -1 }{ x(x - 1) }\] , right? Or am I missing something?

Answer 12

Okay, that definitely can't be right. Out of four options I'm given, this isn't one of them.

Answer 13

Woops, make sure you distribute the subtraction to each term in the brackets.

Answer 14

Whoops, okay! Thank you so much for your help!

Answer 15

Figure it out? :)
np