# 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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 Click here to see ALL problems on Polynomials-and-rational-expressions 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)   (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.