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

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> 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      Log On


   

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) About Me  (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) About Me  (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!
%28%28x%5E2+-+9%29%2F%28x+%2B+1%29%29%2F%28%28x%2B3%29%2F%28x%5E2-1%29%29

The easiest and LEAST confusing way to continue with this is to separate the 2 fractions as follows:

%28x%5E2+-+9%29%2F%28x+%2B+1%29 ÷ %28x+%2B+3%29%2F%28x%5E2+-+1%29 ------ I'm sure this looks a lot less confusing now!!

%28%28x+-+3%29%28x+%2B+3%29%29%2F%28x+%2B+1%29 ÷ %28x+%2B+3%29%2F%28%28x+-+1%29%28x+%2B+1%29%29 ----- Factoring x%5E2+-+9 and x%5E2+-+1

%28%28x+-+3%29%28x+%2B+3%29%29%2F%28x+%2B+1%29 * %28%28x+-+1%29%28x+%2B+1%29%29%2F%28x+%2B+3%29 ----- Changing DIVISION SYMBOL to MULTIPLICATION, and then INVERTING DIVISOR

%28%28x+-+3%29cross%28%28x+%2B+3%29%29%29%2Fcross%28%28x+%2B+1%29%29 * %28%28x+-+1%29cross%28%28x+%2B+1%29%29%29%2Fcross%28%28x+%2B+3%29%29 --- Cancelling numerators and denominators

%28x+-+3%29%28x+-+1%29, or highlight_green%28x%5E2+-+4x+%2B+3%29

You can do the check!! 

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