Your classmate simplified the following rational expression and asked you if you got the same answer. Determine whether the answer below is correct. If it is not correct, simplify the expression. Show all of your work. Rational expression: x squared minus 1, over x squared minus 4x minus 5, divided by 2x squared plus 4 x, over 6x squared minus 30x Your friend's answer: 2x times the quantity x minus 1 times the quantity x plus 2, all over 6x times the quantity x minus 5 times the quantity x minus 5

(1) Answers

[(x²-1)/(x²-4x-5)] / [(2x²+4x)/6x²-30x)]. Each part could be re rewritten as follows: 1) (x²-1) = (x-1)(x+1) 2) (x²-4x-5) = (x-5)(x+1) 3) (2x²+4x) = 2x(x+2) 4) (6x²-30x) = 2x(3x-15) Now replace & you will get (note the a fraction divided by another fraction equal to the PRODUCT of the 1st one by the INVERSE of the 2nd) ahter simplification: 3(x-1) / (x+2)

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