PLEASE HELP! Simplify the rational expressions. State any excluded values. Screenshot included! Medal!

- anonymous

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- anonymous

##### 1 Attachment

- jim_thompson5910

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- jim_thompson5910

the numerator 3x-6 can be factored
3 and 6 have the factor 3 in common, so we can factor out this common factor
3x-6 = 3(x-2)
notice if you were to distribute the 3 back in, you'd get 3x-6

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## More answers

- jim_thompson5910

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at this point, I'm sure you see what to do next

- anonymous

To be quite honest I've never done this math before

- anonymous

cancel out the x's or something? I have no clue

- jim_thompson5910

the `x-2` terms will divide to 1
recall that x/x = 1
in english: "any term, except 0, divided by itself will give you 1"

- jim_thompson5910

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- jim_thompson5910

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- anonymous

okay I think I get it would you help me with the second one?

- jim_thompson5910

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- jim_thompson5910

are you able to factor \[\Large x^2+3x-10\] at all?

- jim_thompson5910

oh and I nearly forgot: for #8, the excluded value is x = 2. This value must be excluded to avoid dividing by zero

- anonymous

wait what?

- anonymous

so the answer is x = 2

- jim_thompson5910

no I'm saying that x = 2 is kicked out because if x = 2, then the denominator x-2 turns to 0 (we can't divide by zero). This is all for #8

- jim_thompson5910

\[\Large \frac{3x-6}{x-2}\] simplifies to 3 (as shown above in the drawings). The restriction is that \(\large x\ne 2\)

- jim_thompson5910

make sense?

- anonymous

yes!

- jim_thompson5910

ok onto #9

- jim_thompson5910

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- anonymous

no like I don't get how to do it?

- jim_thompson5910

think of 2 numbers that multiply to -10 AND add to +3

- anonymous

if you showed me how to do it step by step 1.) 2.) 3.) I would know how to do it

- anonymous

-2 * 5?

- jim_thompson5910

yes,
-2*5 = -10
-2+5 = 3

- jim_thompson5910

since the two numbers are -2 and 5, this means x^2+3x-10 factors to (x-2)(x+5)

- anonymous

so x-2/-2*5=3?

- jim_thompson5910

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- jim_thompson5910

like in #8, the `x-2` terms divide to 1 and cancel out effectively
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- anonymous

oh

- jim_thompson5910

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- jim_thompson5910

so hopefully you see how
\[\Large \frac{x-2}{x^2+3x-10} = \frac{1}{x+5}\]
the restrictions are that \(\large x \ne 2\) or \(\large x \ne -5\) to avoid division by zero errors

- anonymous

I get it a little now it will just take me more practice

- jim_thompson5910

here's a page that offers more practice
http://www.purplemath.com/modules/rtnldefs2.htm

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