1. ## Am I wrong or are the answers off?

They say the answers for 25, and 28 are both 0 but that's not what I get. Can someone please verify this. Thanks.

2. ## Re: Am I wrong or are the answers off?

Herllo, thatsmessedup!

You are right!

They say the answers for 25 and 28 are both 0. . They are wrong!.

$\displaystyle 25.\;\frac{x}{x-1} - \frac{x}{1-x}$

$\displaystyle \frac{x}{x-1} - \frac{x}{1-x} \;=\;\frac{x}{x-1} - \frac{x}{\text{-}(x-1)} \;=\;\frac{x}{x-1} + \frac{x}{x-1} \;=\;\frac{2x}{x-1}$

$\displaystyle 28.\;\frac{1}{(x-1)(x-2)} + \frac{1}{(x-2)(x-3)}$

$\displaystyle \frac{1}{(x-1)(x-2)}\cdot\frac{x-3}{x-3} + \frac{1}{(x-2)(x-3)}\cdot\frac{x-1}{x-1}$

. . . $\displaystyle =\;\frac{x-3}{(x-1)(x-2)(x-3)} + \frac{x-1}{(x-1)(x-2)(x-3)}$

. . . $\displaystyle =\;\frac{(x-3) + (x-1)}{(x-1)(x-2)(x-3)}$

. . . $\displaystyle =\;\frac{2x-4}{(x-1)(x-2)(x-3)}$

. . . $\displaystyle =\;\frac{2(x-2)}{(x-1)(x-2)(x-3)}$

. . . $\displaystyle =\;\frac{2}{(x-1)(x-3)}$

3. ## Re: Am I wrong or are the answers off?

Originally Posted by Soroban
Herllo, thatsmessedup!

You are right!

$\displaystyle \frac{x}{x-1} - \frac{x}{1-x} \;=\;\frac{x}{x-1} - \frac{x}{\text{-}(x-1)} \;=\;\frac{x}{x-1} + \frac{x}{x-1} \;=\;\frac{2x}{x-1}$

$\displaystyle \frac{1}{(x-1)(x-2)}\cdot\frac{x-3}{x-3} + \frac{1}{(x-2)(x-3)}\cdot\frac{x-1}{x-1}$

. . . $\displaystyle =\;\frac{x-3}{(x-1)(x-2)(x-3)} + \frac{x-1}{(x-1)(x-2)(x-3)}$

. . . $\displaystyle =\;\frac{(x-3) + (x-1)}{(x-1)(x-2)(x-3)}$

. . . $\displaystyle =\;\frac{2x-4}{(x-1)(x-2)(x-3)}$

. . . $\displaystyle =\;\frac{2(x-2)}{(x-1)(x-2)(x-3)}$

. . . $\displaystyle =\;\frac{2}{(x-1)(x-3)}$
Of course, this is implying that \displaystyle \displaystyle \begin{align*} x \neq \left\{ 1, 2, 3 \right\} \end{align*}.

4. ## Re: Am I wrong or are the answers off?

Originally Posted by Prove It
Of course, this is implying that \displaystyle \displaystyle \begin{align*} x \neq \left\{ 1, 2, 3 \right\} \end{align*}.
Still means that the answer will never be 0, right?

5. ## Re: Am I wrong or are the answers off?

Originally Posted by Paze
Still means that the answer will never be 0, right?
Yes

6. ## Re: Am I wrong or are the answers off?

I'm actually get this practice exam from here Glendale Community College : Sample Tests and Study Packets which is ridiculous!