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
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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)
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