SOLUTION: Need help simplify this rational expression. Thanks. (a^3-b^3) / (a^2-b^2) How did the back of the book get their answer? (a^2+ab+b^2) / (a+b)

Algebra ->  Rational-functions -> SOLUTION: Need help simplify this rational expression. Thanks. (a^3-b^3) / (a^2-b^2) How did the back of the book get their answer? (a^2+ab+b^2) / (a+b)      Log On


   

Question 62597This question is from textbook
: Need help simplify this rational expression. Thanks. (a^3-b^3) / (a^2-b^2)
How did the back of the book get their answer? (a^2+ab+b^2) / (a+b) This question is from textbook

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%5E3-b%5E3%29+%2F+%28a%5E2-b%5E2%29
looking at the numerator, note that
%28a%5E2+-+b%5E2%29%28a+%2B+b%29+=+a%5E3+-+ab%5E2+%2B+a%5E2b+-+b%5E3
add %2B+ab%5E2+-+a%5E2b to both sides
%28a%5E2+-+b%5E2%29%28a+%2B+b%29+%2B+ab%5E2+-+a%5E2b+=+a%5E3+-+b%5E3
substitute in original equation
%28%28a%5E2+-+b%5E2%29%28a+%2B+b%29+%2B+ab%5E2+-+a%5E2b%29+%2F+%28a%5E2+-+b%5E2%29

a+%2B+b+-+%28%28a%5E2b+-+ab%5E2%29+%2F+%28a%5E2+-+b%5E2%29%29
a+%2B+b+-+%28a%5E2b+-+ab%5E2%29+%2F+%28%28a+%2B+b%29%28a+-+b%29%29%29
a+%2B+b+-+%28%28ab%28a+-+b%29%29+%2F+%28%28a+%2B+b%29%28a+-+b%29%29%29
a+%2B+b+-+%28ab+%2F+%28a+%2B+b%29%29
multiply %28a+%2B+b%29 times %28a+%2B+b%29+%2F+%28a+%2B+b%29
%28a+%2B+b%29%28a+%2B+b%29+%2F+%28a+%2B+b%29+-+%28ab+%2F+%28a+%2B+b%29%29
%28%28a+%2B+b%29%5E2+-+ab%29+%2F+%28a+%2B+b%29
%28a%5E2+%2B+2ab+%2B+b%5E2+-+ab%29+%2F+%28a+%2B+b%29
%28a+%5E2+%2B+ab+%2B+b%5E2%29+%2F+%28a+%2B+b%29 which is the book's answer