SOLUTION: This question is from my ACT Math Study book. I'm having trouble understanding the steps to find the answer. The Question says: Simplify: ((x^2-9)/(x+1)) / ((x+3)/(x^2-1)) (i

Question 935835: This question is from my ACT Math Study book. I'm having trouble understanding the steps to find the answer.
The Question says:
Simplify: ((x^2-9)/(x+1)) / ((x+3)/(x^2-1))
(its written as a fraction divided by the second as a fraction)
I know the first thing to do is flip the second fraction and then multiply, so I did this and got: (x^2-9)(x^2-1) over (x+1)(x+3). I then FOILed the top and bottom to get: (x^4-10x^2+9) over (x^2 +4x +3). Then I thought I could reduce to: x^4-9x^2+6 over 4x. This answer is wrong.
The solution in the book is exactly this:
((x^2-9)/(x+1)) / ((x+3)/(x^2-1)) = ((x+3)(x-3)/(x+1))*((x+1)(x-1)/(x+3))=(x-3)(x-1)=x^2-4x+3.
I'm not following the steps that the book used to come up with this answer, and am wondering why my approach is incorrect. Thank You for your help!

Found 2 solutions by richard1234, MathTherapy:
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
In short: you can't reduce fractions like that. You can divide top and bottom by the same number/expression to obtain an equivalent expression, but your reduction is incorrect.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

This question is from my ACT Math Study book. I'm having trouble understanding the steps to find the answer.
The Question says:
Simplify: ((x^2-9)/(x+1)) / ((x+3)/(x^2-1))
(its written as a fraction divided by the second as a fraction)
I know the first thing to do is flip the second fraction and then multiply, so I did this and got: (x^2-9)(x^2-1) over (x+1)(x+3). I then FOILed the top and bottom to get: (x^4-10x^2+9) over (x^2 +4x +3). Then I thought I could reduce to: x^4-9x^2+6 over 4x. This answer is wrong.
The solution in the book is exactly this:
((x^2-9)/(x+1)) / ((x+3)/(x^2-1)) = ((x+3)(x-3)/(x+1))*((x+1)(x-1)/(x+3))=(x-3)(x-1)=x^2-4x+3.
I'm not following the steps that the book used to come up with this answer, and am wondering why my approach is incorrect. Thank You for your help!

The easiest and LEAST confusing way to continue with this is to separate the 2 fractions as follows:
� ------ I'm sure this looks a lot less confusing now!!
� ----- Factoring and
* ----- Changing DIVISION SYMBOL to MULTIPLICATION, and then INVERTING DIVISOR
* --- Cancelling numerators and denominators
, or
You can do the check!!
===================
Send comments, �thank-yous,� and inquiries to �D� at MathMadEzy@aol.com.
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