SOLUTION: Add or subtract as indicated, Simplify. Show factoring, cancelling, and the steps to finding the lowest common denominator. (Assume that no denominator is 0.) (x+5)(2)/x(2)

Algebra ->  Expressions -> SOLUTION: Add or subtract as indicated, Simplify. Show factoring, cancelling, and the steps to finding the lowest common denominator. (Assume that no denominator is 0.) (x+5)(2)/x(2)      Log On


   

Question 349727: Add or subtract as indicated, Simplify. Show factoring, cancelling, and the steps to finding the lowest common denominator. (Assume that no denominator is 0.)

(x+5)(2)/x(2)+2x-15 + 2/4x-12
I really need help very soon, I am stuck and don't even know where to begin. Thank you! :)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x%2B5%29%5E2%29%2F%28x%5E2%2B2x-15%29%2B2%2F%284x-12%29 Start with the given expression.


%28%28x%2B5%29%28x%2B5%29%29%2F%28x%5E2%2B2x-15%29%2B2%2F%284x-12%29 Break up the first numerator


%28%28x%2B5%29%28x%2B5%29%29%2F%28%28x%2B5%29%28x-3%29%29%2B2%2F%284x-12%29 Factor the first denominator.


Highlight the common terms.


Cancel out the common terms.


%28x%2B5%29%2F%28x-3%29%2B2%2F%284x-12%29 Simplify


%28x%2B5%29%2F%28x-3%29%2B2%2F%284%28x-3%29%29 Factor the second denominator.


Take note that the LCD is 4%28x-3%29. So we need to get every denominator equal to the LCD so we can add the fractions.


%284%28x%2B5%29%29%2F%284%28x-3%29%29%2B2%2F%284%28x-3%29%29 Multiply the first fraction by 4%2F4 to get that fraction to have the denominator equal to the LCD.


%284x%2B20%29%2F%284x-12%29%2B2%2F%284x-12%29 Distribute.


%284x%2B20%2B2%29%2F%284x-12%29 Add the fractions.


%284x%2B22%29%2F%284x-12%29 Combine like terms.


%282%282x%2B11%29%29%2F%284x-12%29 Factor out a '2' from the numerator.


%282%282x%2B11%29%29%2F%282%282x-6%29%29 Factor out a '2' from the denominator.


%28highlight%282%29%282x%2B11%29%29%2F%28highlight%282%29%282x-6%29%29 Highlight the common terms.


%28cross%282%29%282x%2B11%29%29%2F%28cross%282%29%282x-6%29%29 Cancel out the common terms.


%282x%2B11%29%2F%282x-6%29 Simplify.


So %28%28x%2B5%29%5E2%29%2F%28x%5E2%2B2x-15%29%2B2%2F%284x-12%29 simplifies to %282x%2B11%29%2F%282x-6%29


In other words, %28%28x%2B5%29%5E2%29%2F%28x%5E2%2B2x-15%29%2B2%2F%284x-12%29=%282x%2B11%29%2F%282x-6%29


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim