# Simplifying, Finding Domain of Rational Expressions

#### skaterchicky23

##### New member
I'm having some issues with this question if anyone could help me out

-x 2x-1
----------- - -----------
X^2-3x+2 x^2-2x+1

I simplified it to:

-x (2x-1)
----------- - -----------
(x-2)(x-1) (x-1)(x-1)

How would I further simplify this and how would i do the subtraction?

I have a domain of 1/2,1, 2
but I am not sure what the domain of -x would be.

#### stapel

##### Super Moderator
Staff member
skaterchicky23 said:
I'm having some issues with this question if anyone could help me out

-x/(x^2 - 3x + 2) - (2x - 1)/(x^2 - 2x + 1)

I simplified it to:

-x/[(x - 2)(x - 1)] - (2x - 1)/[(x - 1)(x - 1)]
I'm not sure what you mean by "simplified", since factoring is almost always regarded as the opposite of simplification...? Do you perhaps mean "I've factored the denominators, but don't know what to do next, with respect to finding a common denominator and then combining the two fractions"...?

skaterchicky23 said:
I have a domain of 1/2,1, 2
Do you perhaps mean that you have the domain of the related function as being all x other than the listed values...? Which denominator gave you the excluded value of "x = 1/2"?

skaterchicky23 said:
but I am not sure what the domain of -x would be.
Why would the domain of f(x) = -x come into play...? Or is this another exercise...?

Eliz.

#### galactus

##### Super Moderator
Staff member
Do it like as if you were subtracting a regular numerical fraction.

The LCD is (x-1)(x-1)(x-2)

Multiply the top and bottom of the left side by x-1 and the right side by x-2 as to get the denominators the same.

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

Can you continue?.

BTW, Everything but 1 and 2 are in the domain.

#### skaterchicky23

##### New member
Hi Thanks Galactus,
that helps a lot,

I can continue from there with simplifying, I'm a little confused about the domain, for 2x-1, would that not make 1/2 part of what x could not equal?

or is this not right? if not could you let me know why, i'm getting a little confused on that part

#### Subhotosh Khan

##### Super Moderator
Staff member
skaterchicky23 said:
I'm having some issues with this question if anyone could help me out
Code:
     -x              2x-1
-----------   -   -----------
X^2-3x+2        x^2-2x+1

I simplified it to:

-x                (2x-1)
-----------   -   -----------
(x-2)(x-1)       (x-1)(x-1)

___________________________________________________
If you had to simplify the following expression:

$$\displaystyle \frac{3}{2\cdot 5} - \frac{7}{5\cdot 5}$$

You find LCD and

$$\displaystyle = \, \frac{3 \cdot 5}{2\cdot 5 \cdot 5} - \frac{7 \cdot 2}{5\cdot 5 \cdot 2}$$

$$\displaystyle = \, \frac{3 \cdot 5 - 7 \cdot 2}{2\cdot 5 \cdot 5}$$

$$\displaystyle = \, \frac{1}{50}$$

_________________________________________________________

How would I further simplify this and how would i do the subtraction?

I have a domain of 1/2,1, 2
but I am not sure what the domain of -x would be.

For simplification - you do not need worry about domain

#### skaterchicky23

##### New member
Hi,
Should this give me a simplified answer of (x^2)9x-4
------------
x^3

I'm really struggling with this right now so any help would be great, especially if I have gone down a wrong path

I got this answer by following the steps in the reply from Galactus and then getting

-3x^2+6x-2
--------------
(x-1)(x-1)(x-2)

then

-3x^2+6x-2
___________________
x^3-4x2-3x+2

For this question the teacher has requested that we provide them with the domain, would that be .5,1,2 ?

#### galactus

##### Super Moderator
Staff member
That's good enough. 'bout as far as you can take it.

$$\displaystyle \frac{-3x^{2}+6x-2}{(x-2)(x-1)^{2}}$$

To find what is not in the domain, look for what results in division by 0. Everything else is in the domain.