SOLUTION: i have a few questions. It mostly relates to adding and subtracting fractions with some multiplication. i says to simplify, but it is hard for me. HELP!!! I'll provide the problem/

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: i have a few questions. It mostly relates to adding and subtracting fractions with some multiplication. i says to simplify, but it is hard for me. HELP!!! I'll provide the problem/      Log On


   

Question 118604This question is from textbook Algebra: structure and Method: book 1
: i have a few questions. It mostly relates to adding and subtracting fractions with some multiplication. i says to simplify, but it is hard for me. HELP!!! I'll provide the problem/answers (because they are in the back of the book)like this. equation= answer
33. 2/x-3 + 4/x+3 = 6(x-1)/(x-3)(x+3)
35. 4/x+1 - 1/x-2 = 3(x-3)/(x+1)(x-2)
37. 2y/(y-5)(y+5) - y/y-5 = -y(y+3)/(y-5)(y+5)
39. x/x+y + y/x-y = x^2 + y^2/(x+y)(x-y) This question is from textbook Algebra: structure and Method: book 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to help you get started.

#33

%282%29%2F%28x-3%29%2B%284%29%2F%28x%2B3%29 Start with the given expression




Since the denominators are not equal, we need to get them to a common denominator. Since the LCD is %28x-3%29%28x%2B3%29, we need to get each denominator to %28x-3%29%28x%2B3%29




%28%28%28x%2B3%29%29%2F%28%28x%2B3%29%29%29%28%282%29%2F%28x-3%29%29%2B%284%29%2F%28x%2B3%29 Multiply %282%29%2F%28x-3%29 by %28%28x%2B3%29%29%2F%28%28x%2B3%29%29



%28x%2B3%29%282%29%2F%28%28x-3%29%28x%2B3%29%29%2B%284%29%2F%28x%2B3%29 Combine the fractions



Multiply %284%29%2F%28x%2B3%29 by %28%28x-3%29%29%2F%28%28x-3%29%29



Combine the fractions



%28%28x%2B3%29%282%29%2B%28x-3%29%284%29%29%2F%28x-3%29%28x%2B3%29 Since the 2 fractions have the common denominator %28x-3%29%28x%2B3%29, we can combine them. In order to do that, just combine the numerators.


%282x%2B6%2B4x-12%29%2F%28x-3%29%28x%2B3%29 Distribute


%286x-6%29%2F%28x-3%29%28x%2B3%29 Combine like terms


6%28x-1%29%2F%28x-3%29%28x%2B3%29 Now factor out the GCF 6 from the numerator


So %282%29%2F%28x-3%29%2B%284%29%2F%28x%2B3%29 simplifies to 6%28x-1%29%2F%28x-3%29%28x%2B3%29






#35




%284%29%2F%28x%2B1%29-%281%29%2F%28x-2%29 Start with the given expression




Since the denominators are not equal, we need to get them to a common denominator. Since the LCD is %28x%2B1%29%28x-2%29, we need to get each denominator to %28x%2B1%29%28x-2%29




%28%28%28x-2%29%29%2F%28%28x-2%29%29%29%28%284%29%2F%28x%2B1%29%29%2B%281%29%2F%28x-2%29 Multiply %284%29%2F%28x%2B1%29 by %28%28x-2%29%29%2F%28%28x-2%29%29



%28x-2%29%284%29%2F%28%28x%2B1%29%28x-2%29%29%2B%281%29%2F%28x-2%29 Combine the fractions



Multiply %281%29%2F%28x-2%29 by %28%28x%2B1%29%29%2F%28%28x%2B1%29%29



Combine the fractions



%28%28x-2%29%284%29-%28x%2B1%29%281%29%29%2F%28x%2B1%29%28x-2%29 Since the 2 fractions have the common denominator %28x%2B1%29%28x-2%29, we can combine them. In order to do that, just combine the numerators.


%284x-8-x-1%29%2F%28x%2B1%29%28x-2%29 Distribute



%283x-9%29%2F%28x%2B1%29%28x-2%29 Combine like terms



3%28x-3%29%2F%28x%2B1%29%28x-2%29 Factor out 3 from the numerator


So %284%29%2F%28x%2B1%29-%281%29%2F%28x-2%29 simplifies to 3%28x-3%29%2F%28x%2B1%29%28x-2%29