SOLUTION: Can anyone help me out with this problem? 4x + 8 _______ I started to work the problem out and couldnt get any 5x - 15 further. I know 4x + 8 is e

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can anyone help me out with this problem? 4x + 8 _______ I started to work the problem out and couldnt get any 5x - 15 further. I know 4x + 8 is e      Log On


   

Question 127505: Can anyone help me out with this problem?
4x + 8
_______ I started to work the problem out and couldnt get any
5x - 15 further. I know 4x + 8 is equal to 4(x+2) and so on,
_______ that is as far as I got. Thank You
12x+ 24
_______
10x - 30
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%284x%2B8%29%2F%285x-15%29%29%2F%28%2812x%2B24%29%2F%2810x-30%29%29 Start with the given expression

%28%284x%2B8%29%2F%285x-15%29%29%2A%28%2810x-30%29%2F%2812x%2B24%29%29 Multiply the first fraction by the reciprocal of the second fraction


%28%284%28x%2B2%29%29%2F%285x-15%29%29%28%2810x-30%29%2F%2812x%2B24%29%29 Factor 4x%2B8 to get 4%28x%2B2%29

%28%284%28x%2B2%29%29%2F%285%28x-3%29%29%29%28%2810x-30%29%2F%2812x%2B24%29%29 Factor 5x-15 to get 5%28x-3%29

%28%284%28x%2B2%29%29%2F%285%28x-3%29%29%29%28%2810%28x-3%29%29%2F%2812x%2B24%29%29 Factor 10x-30 to get 10%28x-3%29

%28%284%28x%2B2%29%29%2F%285%28x-3%29%29%29%28%2810%28x-3%29%29%2F%2812%28x%2B2%29%29%29 Factor 12x%2B24 to get 12%28x%2B2%29


4%28x%2B2%2910%28x-3%29%2F5%28x-3%2912%28x%2B2%29 Combine the fractions


4cross%28x%2B2%2910cross%28x-3%29%2F5cross%28x-3%2912cross%28x%2B2%29 Cancel like terms


%284%2A10%29%2F%285%2A12%29 Simplify


40%2F60 Multiply


2%2F3 Reduce




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Answer:
So %28%284x%2B8%29%2F%285x-15%29%29%2F%28%2812x%2B24%29%2F%2810x-30%29%29 simplifies to 2%2F3


In other words, %28%284x%2B8%29%2F%285x-15%29%29%2F%28%2812x%2B24%29%2F%2810x-30%29%29=2%2F3