Multiplying Algebraic Fractions

Date: 11/05/2002 at 00:57:22
From: Lizet
Subject: Multiplying and dividing algebraic fractions

Perform the indicated operation and simplify:

x^2+8x+7     x^2+2x-3
-------- . ----------
  x^2-1     x^2+10x+21

The answer is 1, but I don't know how to get it.

Date: 11/05/2002 at 19:08:35
From: Doctor Ian
Subject: Re: Multiplying and dividing algebraic fractions

Hi Lizet,

The key is to factor the quadratic expressions, so you can get
binomials that cancel each other out. 

Let's look at an operation similar to yours:

      x^2-5x+6     x^2+6x+5
   = ---------- * ----------
      x^2-x-2      x^2+2x-15


     (x-2)(x-3)   (x+1)(x+5)
   = ---------- * ----------
     (x+1)(x-2)   (x-3)(x+5)


     (x+1)(x-2)(x-3)(x+5)
   = --------------------
     (x+1)(x-2)(x-3)(x+5)


   = 1

Does this help?

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/