SOLUTION: this problem is on page 407. 1/2 +1/4x --------- = I didn't get the same answer as the back of the book. It's x/3 - 1/12x supposed to be 3/2x-1. I don't understand how

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: this problem is on page 407. 1/2 +1/4x --------- = I didn't get the same answer as the back of the book. It's x/3 - 1/12x supposed to be 3/2x-1. I don't understand how      Log On


   

Question 141385This question is from textbook Elementary and Intermediate Algebra
: this problem is on page 407.
1/2 +1/4x
--------- = I didn't get the same answer as the back of the book. It's
x/3 - 1/12x supposed to be 3/2x-1. I don't understand how they got that. Anne This question is from textbook Elementary and Intermediate Algebra

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!

Hi Anne. Let's first look at the numerator:
(1/2)+(1/4x) We'll multiply each term by (4x/4x) and we get
(2x+1)/4x
Now lets look at the denominator:
(x/3)-(1/12x) We'll multiply each term by (12x/12x) and we get
(4x^2-1)/12x but 4x^2-1=(2x+1)(2x-1) so now we have
((2x+1)(2x-1))/12x
now let's put the numerator and denominator back together again:
%28%282x%2B1%29%2F4x%29%2F%28%282x%2B1%29%282x-1%29%2F12x%29
Now we'll multiply both the numerator and denominator by 12x/((2x-1)(2x+1))
and we get:
((2x+1)/4x)*12x/((2x-1)(2x+1))/1 and this gives us
3/(2x-1)

Hope this helps---ptaylor