SOLUTION: Perform the indicated operations and simplify the following expression: {{{(((6r^2-7r-3)/(r^2-1)) /((4r^2-12r+9)/(r^2-1))) * ((2r^2-r-3)/(3r^2-2r-1))}}} A) {{{(2r-3)^2 /(3r+1

Algebra ->  Algebra  -> Rational-functions -> SOLUTION: Perform the indicated operations and simplify the following expression: {{{(((6r^2-7r-3)/(r^2-1)) /((4r^2-12r+9)/(r^2-1))) * ((2r^2-r-3)/(3r^2-2r-1))}}} A) {{{(2r-3)^2 /(3r+1      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 145604: Perform the indicated operations and simplify the following expression:
%28%28%286r%5E2-7r-3%29%2F%28r%5E2-1%29%29+%2F%28%284r%5E2-12r%2B9%29%2F%28r%5E2-1%29%29%29+%2A+%28%282r%5E2-r-3%29%2F%283r%5E2-2r-1%29%29
A) %282r-3%29%5E2+%2F%283r%2B1%29
B) %28r%2B1%29%2F%28r-1%29
C) %28r-1%29%2F%28r%2B1%29
D) 1
Answer by Edwin McCravy(6938) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28%286r%5E2-7r-3%29%2F%28r%5E2-1%29%29+%2F%28%284r%5E2-12r%2B9%29%2F%28r%5E2-1%29%29%29+%2A+%28%282r%5E2-r-3%29%2F%283r%5E2-2r-1%29%29

Invert the second fraction in the first parentheses
and multiply:

%28%28%286r%5E2-7r-3%29%2F%28r%5E2-1%29%29%28%28r%5E2-1%29%2F%284r%5E2-12r%2B9%29%29%29+%2A+%28%282r%5E2-r-3%29%2F%283r%5E2-2r-1%29%29

Cancel the r%5E2-1's

%28%28%286r%5E2-7r-3%29%2Fcross%28r%5E2-1%29%29%28cross%28r%5E2-1%29%2F%284r%5E2-12r%2B9%29%29%29+%2A+%28%282r%5E2-r-3%29%2F%283r%5E2-2r-1%29%29

%28%286r%5E2-7r-3%29%2F%284r%5E2-12r%2B9%29%29+%2A+%28%282r%5E2-r-3%29%2F%283r%5E2-2r-1%29%29

Factor all the numerators and denominators:

%28%28%282r-3%29%283r%2B1%29%29%2F%28%282r-3%29%282r-3%29%29%29%28%28%282r-3%29%28r%2B1%29%29%2F%283r%2B1%29%28r-1%29%29%29++

Cancel the %282r-3%29's

%28%28cross%28%282r-3%29%29%283r%2B1%29%29%2F%28cross%28%282r-3%29%29%282r-3%29%29%29%28%28%282r-3%29%28r%2B1%29%29%2F%283r%2B1%29%28r-1%29%29%29++

Cancel the %283r%2B1%29's

%28%28cross%28%282r-3%29%29cross%28%283r%2B1%29%29%29%2F%28cross%28%282r-3%29%29%282r-3%29%29%29%28%28%282r-3%29%28r%2B1%29%29%2Fcross%28%283r%2B1%29%29%28r-1%29%29%29++ 

Cancel the %282r-3%29's

%28%28cross%28%282r-3%29%29cross%28%283r%2B1%29%29%29%2F%28cross%28%282r-3%29%29cross%28%282r-3%29%29%29%29%28%28cross%28%282r-3%29%29%28r%2B1%29%29%2Fcross%28%283r%2B1%29%29%28r-1%29%29%29++ 

%28r%2B1%29%2F%28r-1%29, which is choice B)

Edwin