SOLUTION: Can you explain to me in a simple way how or a step by step way to evaluate rational expressions? Chapter 7.1 exercise # 52. 3x^2+8x+4 over 3x^2-4x-4 Chapter 7.3 # 41. 3

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Question 59160This question is from textbook beginning algebra
: Can you explain to me in a simple way how or a step by step way to evaluate rational expressions?
Chapter 7.1 exercise
# 52. 3x^2+8x+4 over 3x^2-4x-4
Chapter 7.3
# 41. 3 over k^2+5k with a comma between
2 over k^2+3k-10
Thanks for any help you can give.
This question is from textbook beginning algebra

Answer by stanbon(57347) About Me  (Show Source):
You can put this solution on YOUR website!
# 52. 3x^2+8x+4 over 3x^2-4x-4
You need to be able to factor these in order to
simplify the fraction.
Numerator factoring goes as follows:
3x^2+8x+4
=3x^2+6x+2x+4
=3x(x+2)+2(x+2)
=(x+2)(3x+2)
-------------------
Denominator factoring goes as follows:
3x^2-4x-4
=3x^2-6x+2x-4
=3x(x-2)+2(x-2)
=(x-2)(3x+2)
---------------------------
If you write the factored form of the numerator
over the factored form of the denominator you
see there is a common factor of (3x+2); these
cancel and you are let with the following:
(x+2)/(x-2)
---------
That is the simplified form of the original
fraction.
------------------------------------------------
Chapter 7.3
# 41. 3 over k^2+5k with a comma between
2 over k^2+3k-10
(k^2+5k)/(k^2+3k-10)
Factor where you can to get:
=[k(k+5)]/[(k+5)(k-2)
=k/(k-2)
Cheers,
Stan H.