SOLUTION: How do I add 3/x+5 + 4/x-4 could you please show the steps taken.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do I add 3/x+5 + 4/x-4 could you please show the steps taken.      Log On


   

Question 200158This question is from textbook Algebra 1
: How do I add 3/x+5 + 4/x-4 could you please show the steps taken. This question is from textbook Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Take note that the LCD is %28x%2B5%29%28x-4%29


3%2F%28x%2B5%29%2B4%2F%28x-4%29 Start with the given expression.


%283%28x-4%29%29%2F%28%28x%2B5%29%28x-4%29%29%2B4%2F%28x-4%29 Multiply both the numerator and denominator of the first fraction by x-4 (to get this denominator equal to the LCD)


%283x-12%29%2F%28%28x%2B5%29%28x-4%29%29%2B4%2F%28x-4%29 Distribute


%283x-12%29%2F%28%28x%2B5%29%28x-4%29%29%2B%284%28x%2B5%29%29%2F%28%28x%2B5%29%28x-4%29%29 Multiply both the numerator and denominator of the second fraction by x%2B5 (to get this denominator equal to the LCD)


%283x-12%29%2F%28%28x%2B5%29%28x-4%29%29%2B%284x%2B20%29%2F%28%28x%2B5%29%28x-4%29%29 Distribute


%283x-12%2B4x%2B20%29%2F%28%28x%2B5%29%28x-4%29%29 Combine the fractions. This is now possible because the denominators are equal.


%287x%2B8%29%2F%28%28x%2B5%29%28x-4%29%29 Combine like terms.


%287x%2B8%29%2F%28x%5E2%2Bx-20%29 FOIL



So 3%2F%28x%2B5%29%2B4%2F%28x-4%29=%287x%2B8%29%2F%28x%5E2%2Bx-20%29