Turning an Equation Upside-Down

Date: 07/09/2001 at 21:31:17
From: Judy Fontenot
Subject: Turning an equation upside down

I am trying to help a neighbor. There is an example in the book that 
I do not understand. After this step:

2/h = (a + b)/ab, 

the book shows this: 

h/2 = (ab)/(a + b). 

Can you simply invert the fractions and maintain the equivalency? Or 
is there something you do to both sides to accomplish this? 

Thanks for your help.

Date: 07/09/2001 at 23:30:16
From: Doctor Peterson
Subject: Re: Turning an equation upside down

Hi, Judy.

Yes, as long as you know that the values are non-zero, you can take 
the reciprocal of both sides of an equation to get an equivalent 
equation. This is just a shortcut for the following:

    A = B                given
    A / (AB) = B / (AB)  dividing by AB
    1/B = 1/A            simplifying

As long as A and B are non-zero, this is all legal.

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