Question

Simplify the rational expression. State any excluded values.

Answer 1

\[\frac{ x-2 }{ x ^{2}+3x-10 }\]

Answer 2

Factor the bottom:
\[\frac{ x-2 }{ (x-2)(x+5) }\]

Answer 3

I got that and I dont know where to go from there.

Answer 4

cancell x-2

Answer 5

Cancel like terms so you get:
\[\frac{ 1 }{ x+5 }\]
There is a hole at x=2

Answer 6

Now to find the remaining restrictions just set the denominator equal to 0 and solve.

Answer 7

Ok thanks

Answer 8

Yup

Answer 9

Hold on how did you go from \[x ^{2}+3x-10 \to (x-2)(x+5) i got (x+3x)(x-10)\]

Answer 10

How did you get that? :/

Answer 11

I used the distributive prop for binomials.

Answer 12

The distributive property states:
\(a(b + c) = ab + ac\)

For binomials this is usually called FOIL, and is a reference to how you multiply two binomials. I am not sure how you got to the idea that would let you factor them. Factoring and multiplying are related, but not that way. You could call factoring un-multiplying.

The distributive property on a binomial:\[\qquad \;\;\; (x + y)(x + 2y)\\
\implies (x + y)x + (x + y)(2y)\\
\implies x^2+xy +2xy 2y^2\\
\implies x^2 + 3xy +2y^2\]
What you want to look into is this:
http://www.purplemath.com/modules/factquad.htm

Answer 13

Thank you I will look into it.

Answer 14

@e.mccormick I get how it factors down to \[(x-2)(x-5)\] how would I go about finding the excluded value.

Answer 15

Excluded values are anything that would make the denominator into 0.

Answer 16

So it would be +5?

Answer 17

Ummm... \((x-5)\) how did you get that? As Luigi0210 stated, it is \((x+5)\)

And for a visual
https://www.desmos.com/calculator/tbvkmnzgbv