SOLUTION: I am having so much trouble with these two problems: Simplify the rational expressions: a) -x^2+10x-21/-3x^2+23x-14 (friend told me the answer is 3-x/3x-2 but had difficulty tr

Click here to see ALL problems on Polynomials-and-rational-expressions

Question 401295: I am having so much trouble with these two problems: Simplify the rational expressions:
a) -x^2+10x-21/-3x^2+23x-14 (friend told me the answer is 3-x/3x-2 but had difficulty trying to explain the steps to me)
b) 28x^2-29x+6/-28x^2+50x-12 (didn't ask my friend because of question a's explanation issues)
I thought that I could factor the numerator and denominator separately, then divide them, but Im not sure if that's right. Any help is GREATLY appreciated!
Answer by algebrahouse.com(1659) (Show Source):
You can put this solution on YOUR website!
a) -x^2+10x-21/-3x^2+23x-14

-x^2 + 10x - 21
---------------
-3x^2 + 23x - 14

-1(x^2 - 10x + 21)
----------------- {factored -1 out of top and bottom}
-1(3x^2 - 23x + 14)

(x - 7)(x - 3)
--------------- {cancelled the -1's and factored top and bottom into 2 binomials}
(3x - 2)(x - 7)

x - 3
------ {cancelled x - 7 on top and bottom}
3x - 2

******************************************

b) 28x^2-29x+6/-28x^2+50x-12

28x^2 - 29x + 6
-----------------
-28x^2 + 50x - 12

(7x - 2)(4x - 3)
------------------ {factored -2 out of bottom and top into two binomials}
-2(14x^2 - 25x + 6)

(7x - 2)(4x - 3)
------------------ {factored bottom into two binomials}
-2(7x - 2)(2x - 3)

4x - 3
---------- {cancelled 7x - 2 on top and bottom}
-2(2x - 3)

www.algebrahouse.com