## anonymous one year ago PLEASE HELP! Simplify the rational expressions. State any excluded values. Screenshot included! Medal!

1. anonymous

2. jim_thompson5910

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3. 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

4. jim_thompson5910

|dw:1441070429569:dw| at this point, I'm sure you see what to do next

5. anonymous

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

6. anonymous

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

7. 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"

8. jim_thompson5910

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9. jim_thompson5910

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10. anonymous

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

11. jim_thompson5910

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12. jim_thompson5910

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

13. 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

14. anonymous

wait what?

15. anonymous

so the answer is x = 2

16. 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

17. jim_thompson5910

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

18. jim_thompson5910

make sense?

19. anonymous

yes!

20. jim_thompson5910

ok onto #9

21. jim_thompson5910

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22. anonymous

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

23. jim_thompson5910

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

24. anonymous

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

25. anonymous

-2 * 5?

26. jim_thompson5910

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

27. jim_thompson5910

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

28. anonymous

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

29. jim_thompson5910

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30. jim_thompson5910

like in #8, the x-2 terms divide to 1 and cancel out effectively |dw:1441071502600:dw|

31. anonymous

oh

32. jim_thompson5910

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33. 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

34. anonymous

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

35. jim_thompson5910

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