SOLUTION: Hi I need help with adding and subtracting with unlike denominators. If you could do this 1 problem I would very much appriceate it! 1. (2x+1)/(3x-1) - (x+4)/(x-2) Thank You!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi I need help with adding and subtracting with unlike denominators. If you could do this 1 problem I would very much appriceate it! 1. (2x+1)/(3x-1) - (x+4)/(x-2) Thank You!      Log On


   

Question 74436: Hi I need help with adding and subtracting with unlike denominators. If you could do this 1 problem I would very much appriceate it!
1. (2x+1)/(3x-1) - (x+4)/(x-2)
Thank You!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282x%2B1%29%2F%283x-1%29+-+%28x%2B4%29%2F%28x-2%29+
The LCD is (3x-1)(x-2). So we multiply the terms to get to the LCD
Multiply both terms by a clever form of 1 to get to the LCD

%28%28x-2%29%282x%2B1%29-%283x-1%29%28x%2B4%29%29%2F%28%283x-1%29%28x-2%29%29foil the two sets of parenthesis
%282x%5E2-3x-2-3x%5E2-11x%2B4%29%2F%28%283x-1%29%28x-2%29%29Add like terms
%28-x%5E2-14x%2B2%29%2F%28%283x-1%29%28x-2%29%29There's your simplified answer
Note: you can graph these expressions and you'll see that they're equal
Graph of %28-x%5E2-14x%2B2%29%2F%28%283x-1%29%28x-2%29%29

Graph of %282x%2B1%29%2F%283x-1%29+-+%28x%2B4%29%2F%28x-2%29+
So this shows that they are both equal.