SOLUTION: 58.)Simplify complex fraction, reduce ab +b^2 4ab^5 a + b 6a^2b^4

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Question 163704This question is from textbook Elementary and Intermediate
: 58.)Simplify complex fraction, reduce
ab +b^2
4ab^5
a + b
6a^2b^4
This question is from textbook Elementary and Intermediate

Answer by Edwin McCravy(6932) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28ab+%2Bb%5E2%29%2F%284ab%5E5%29%29%2F%28%28a+%2B+b%29%2F%286a%5E2b%5E4%29%29

Write as a division:

matrix%281%2C3%2C%28ab+%2Bb%5E2%29%2F%284ab%5E5%29%2C%27%F7%27%2C%28a+%2B+b%29%2F%286a%5E2b%5E4%29%29

Invert the second fraction and change the division symbol to
multiplication:

matrix%281%2C3%2C%28ab+%2Bb%5E2%29%2F%284ab%5E5%29%2C%27%D7%27%2C%286a%5E2b%5E4%29%2F%28a%2Bb%29%29

Factor the left numerator by taking out b:

matrix%281%2C3%2C%28b%28a+%2Bb%29%29%2F%284ab%5E5%29%2C%27%D7%27%2C%286a%5E2b%5E4%29%2F%28a%2Bb%29%29

Indicate the multiplication of numerators and denominators:

%28b%28a+%2Bb%296a%5E2b%5E4%29%2F%284ab%5E5%28a%2Bb%29%29

Rearrange the factor on the top and multiply the b
by the b%5E4 getting b%5E5

%286a%5E2b%5E5%28a+%2Bb%29%29%2F%284ab%5E5%28a%2Bb%29%29

Divide the 6 and the 4 by 2

%283a%5E2b%5E5%28a+%2Bb%29%29%2F%282ab%5E5%28a%2Bb%29%29

Divide the a%5E2 in the top by the a in the
bottom, getting a in the top:

%283ab%5E5%28a+%2Bb%29%29%2F%282b%5E5%28a%2Bb%29%29

Cancel the b%5E5 in the top and bottom
Cancel the %28a%2Bb%29 in the top and bottom:

%283a%2Across%28b%5E5%29cross%28%28a+%2Bb%29%29%29%2F%282cross%28b%5E5%29cross%28%28a%2Bb%29%29%29

All that's left is

3a%2F2

Edwin