## anonymous one year ago Simplify completely quantity 8 x minus 16 over quantity x squared minus 13 x plus 22 and find the restrictions on the variable.

1. misty1212

HI!!

2. misty1212

$\huge\frac{8x-16}{x^2-13x+22}$?

3. anonymous

I got x-5/x+1 as my answer but I don't know what the restriction would be

4. misty1212

did you factor the denomiantor?

5. anonymous

yes

6. anonymous

Sorry I meant 8/x-11

7. misty1212

$x^2-13x+22=(x-2)(x-11)$

8. triciaal

factor the denominator again hint 2*11 = 22 and 2 + 11 = 13

9. misty1212

then cancel and you get what you wrote

10. anonymous

But what would be the restrictions?

11. misty1212

so your answer is correct as for the "restrictions" the denominator cannot be zero

12. misty1212

$(x-2)(x-11)=0\\ x=2,x=11$

13. misty1212

so the restrictions are $$x\neq2$$ and $$x\neq 11$$ because if $$x$$ where either of those two numbers, the denominator would be zero, and if you try to divide by zero you will explode

14. anonymous

Ok. I need to ask another one

15. anonymous

Simplify completely quantity x squared plus 4 x minus 45 all over x squared plus 10 x plus 9 and find the restrictions on the variable.

16. misty1212

lol the equation tool below is very useful

17. anonymous

I got x-5/x+1

18. anonymous

Sorry

19. misty1212

$\huge \frac{x^2+4x-45}{x^2+10x+9}$

20. misty1212

21. anonymous

yes:) What would be the restrictions for this one? My answer is x-5/x+1

22. misty1212

repeat as before take the denominator in factored form set it equal to zero, solve for $$x$$

23. anonymous

x=-1?

24. misty1212

you obviously already factored the denominator as $(x+1)(x+9)$ solve $(x+1)(x+9)=0$ and solve for $$x$$

25. anonymous

-1,-9

26. misty1212

bingo

27. misty1212

that is, those are the restricted values

28. anonymous

ohh thank you:)

29. anonymous

That's all for now

30. anonymous

Simplify completely quantity 6 x minus 12 over 10.

31. anonymous

is it 3(x-5)/5