SOLUTION: Please help me to simplify each complex fraction and reduce each answer to lowest terms: 42) 1/3+1/y over y/3-3/y and 50) ab+b^2/4ab^5 over a+b/6a^2b^4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help me to simplify each complex fraction and reduce each answer to lowest terms: 42) 1/3+1/y over y/3-3/y and 50) ab+b^2/4ab^5 over a+b/6a^2b^4       Log On


   

Question 88743: Please help me to simplify each complex fraction and reduce each answer to lowest terms:
42) 1/3+1/y over y/3-3/y

and
50) ab+b^2/4ab^5 over a+b/6a^2b^4

Thank you very much!
Answer by chitra(359) About Me  (Show Source):
You can put this solution on YOUR website!
42) The given expression is:

%281%2F3%29+%2B+%281%2Fy%29 over %28y%2F3%29+-+%283%2Fy%29

==> %28%281%2F3%29+%2B+%281%2Fy%29%29%2F%28%28y%2F3%29+-+%283%2Fy%29%29

Taking LCM on both the numerator and the denominator, we get:


%28%28y+%2B+3%29%2F3y%29%2F%28%28y%5E2+-+9%29%2F3y%29


Simplifying the term in the denominator, we get:


%28%28y+%2B+3%29%2F3y%29%2F%28%28y+-+3%29%28y+%2B+3%29%2F3y%29


This can be written as:


+%28%28y+%2B+3%29%2F3y%29+%2A+%28%283y%29%2F%28y+%2B+3%29%28y+-+3%29%29+


Cancelling out terms, we get:

1%2F%28y+-+3%29


Hence, the solution.


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50) %28ab+%2B+b%5E2%29%2F4ab%5E5 over %28a+%2B+b%29%2F%286a%5E2b%5E4%29


This can be written as:


%28%28ab+%2B+b%5E2%29%2F%284ab%5E5%29%29+%2F%28%28a+%2B+b%29%2F%286a%5E2b%5E4%29%29


Taking "b" as the common factor, we get:


%28b%28a+%2B+b%29%2F%284ab%5E5%29%29+%2F%28%28a+%2B+b%29%2F%286a%5E2b%5E4%29%29


This can be written as:

%28b%28a+%2B+b%29%2F%284ab%5E5%29%29+%2A+%28%286a%5E2b%5E4%29%2F%28a+%2B+b%29%29

Cancelling out common terms, we get:

%283%2F2%29a

Hence, the solution.

Regards
Chitra
Online Math Tutor
chitra@knowledgeonlineservices.com