A Trick for Solving Equations with Fractions

Date: 11/12/95 at 23:24:18
From: Anonymous
Subject: similar triangle

Hi, 

I already wrote down the equation, and I solved for "y" but I 
can't figure out how to do "X".

X+5 = 12+Y = 24
---   ----   --
 X     12    18    To get "Y" I first go 12*24=288.
                   Then I go 288 divided by 18 =16.
                   16 + 12 =28. (done)

To find "X" I go..........
			
                  This is my guess.  x+5 = 24
					       ---   --
					        x    18

1) 24 multiply x to become 24x,and then 18(x+5).  So now it's 
18x +90 divided by 24x.  Now after that I don't know what to do 
next. 

  From Vic

Date: 11/14/95 at 20:21:19
From: Doctor Jeremy
Subject: Re: similar triangle

One trick that comes in handy in cases like this is the fact that:

a   c
- = -    implies that ad = bc.
b   d

You can get that by multiplying both sides by ad.
In your case what that means is from

x+5   24
--- = --  you get 18(x+5)=24x and you can probably take it from there.
 x    18

I've used the ad=bc trick so many times in so many cases I do it 
without thinking.  It's one of those that is often not taught, but 
is really useful.

-Doctor Jeremy,  The Geometry Forum