Reduce the following rational expression to lowest terms, if possible. (If not possible, enter IMPOSSIBLE.)

3x − 9
4x − 16

Question

Reduce the following rational expression to lowest terms, if possible. (If not possible, enter IMPOSSIBLE.)
 
3x − 9
4x − 16

anonymous · Answer

It's a fraction.

hero · Answer

$\dfrac{3x - 9}{4x - 16} = \dfrac{3(x - 3)}{4(x - 4)}$

              $=\dfrac{3}{4} \dot\ \dfrac{x - 3}{x - 4}$
 
              $=\dfrac{3}{4} \dot\ \dfrac{x - 4 + 1}{x - 4}$

              $=\dfrac{3}{4} \left( \dfrac{x - 4}{x - 4} + \dfrac{1}{x - 4}\right)$

              $=\dfrac{3}{4} \left( 1+ \dfrac{1}{x - 4}\right)$

              $=\dfrac{3}{4} + \dfrac{3}{4(x - 4)}$

anonymous · Answer

Specify the restrictions on the variable. (Select all that apply.)

x ≠ 4

x ≠ 16

x ≠ 0

x ≠ 3

x ≠ 9

(Which one would be the answer?) @Hero

hero · Answer

Which one do you think would be the answer? Remember, the denominator cannot equal zero.

anonymous · Answer

I think it was 3 & 4

hero · Answer

What do you mean 3 and 4? There's only one value that x cannot equal. Which is it?

anonymous · Answer

0? I missed school when this was taught, I have no idea, sorry.

hero · Answer

$$4x - 16 \ne 0$$


Solve that to find out what x cannot equal

anonymous · Answer

4

anonymous · Answer

Is that the correct answer? @Hero

hero · Answer

$$x \ne 4$$ is correct, yes

anonymous · Answer

Ok, thank you...the next question, I think I got the answer, but can you see if it's correct for me, please?

anonymous · Answer

The answer is incorrect, I don't think the answer is all the way reduced. @ganeshie8  care to help?

ganeshie8 · Answer

which question ?

hero · Answer

No, it is, I just factored it too much

hero · Answer

The correct answer is 

$$\frac{3(x - 3)}{4(x - 4)}$$

anonymous · Answer

oooooh ! ok Thank you lol I think I had that but didnt understand the second part

ganeshie8 · Answer

The rational expression in question not like below, right ?

$\dfrac{1}{(3x-9)(4x-16)}$

anonymous · Answer

no, the 3x-9 is on top.

ganeshie8 · Answer

good, then $\dfrac{3(x - 3)}{4(x - 4)}$ is the final simplified form

ganeshie8 · Answer

this expression goes crazy when the denominator stuff equals $0$

ganeshie8 · Answer

So, to get the restrictions :  
set the denominator equal to $0$, and solve the variable

anonymous · Answer

Ok, hopefully, I'll remember lol

ganeshie8 · Answer

:) thats one important thing to keep in mind when u deal with solving equations involving rational expressions.

anonymous · Answer

Ok, thank you...Can you help me with the other problem i tagged you in?