SOLUTION: I am completely lost in Algebra. I passed Algebra 104 by the skin of my teeth. I read and look over the sections and examples, but I still don't understand how or why they do w

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Question 187869: I am completely lost in Algebra. I passed Algebra 104 by the skin of my teeth.
I read and look over the sections and examples, but I still don't understand how or why they do work the way they do when solved. Sometimes I can disect a simple problem as to how they came up with the answer, but to do it myself and don't know how to start.
I don't know how to type in the problem with out underlining. Here's one of the problems:
4x-2 / 2x^2 +9x-5 underlined and directly below are these numbers
x^2 - 5x x^2-25
Textbook answer: 2
x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%284x-2%29%2F%28x%5E2-5x%29%29%2F%28%282x%5E2%2B9x-5%29%2F%28x%5E2-25%29%29 Start with the given expression.


%28%284x-2%29%2F%28x%5E2-5x%29%29%28%28x%5E2-25%29%2F%282x%5E2%2B9x-5%29%29 Multiply the first fraction %284x-2%29%2F%28x%5E2-5x%29 by the reciprocal of the second fraction %282x%5E2%2B9x-5%29%2F%28x%5E2-25%29.


%28%282%282x-1%29%29%2F%28x%5E2-5x%29%29%28%28x%5E2-25%29%2F%282x%5E2%2B9x-5%29%29 Factor 4x-2 to get 2%282x-1%29.


%28%282%282x-1%29%29%2F%28x%28x-5%29%29%29%28%28x%5E2-25%29%2F%282x%5E2%2B9x-5%29%29 Factor x%5E2-5x to get x%28x-5%29.


Factor x%5E2-25 to get %28x-5%29%28x%2B5%29.


Factor 2x%5E2%2B9x-5 to get %28x%2B5%29%282x-1%29.


%282%282x-1%29%28x-5%29%28x%2B5%29%29%2F%28x%28x-5%29%28x%2B5%29%282x-1%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


2%2Fx Simplify.


So %28%284x-2%29%2F%28x%5E2-5x%29%29%2F%28%282x%5E2%2B9x-5%29%2F%28x%5E2-25%29%29 simplifies to 2%2Fx.


In other words, %28%284x-2%29%2F%28x%5E2-5x%29%29%2F%28%282x%5E2%2B9x-5%29%2F%28x%5E2-25%29%29=2%2Fx where x%3C%3E-5, x%3C%3E0, x%3C%3E1%2F2, or x%3C%3E5