Solving for x

Date: 1/23/96 at 9:31:0
From: Anonymous
Subject: Solving for x

I need help on this problem:

x/x+4 = x+1/x+8    Solve for x.

Thanks for the help!

Date: 6/14/96 at 14:31:35
From: Doctor Chaos
Subject: Re: Solving for x

This problem can be solved by setting it up as fractions and cross 
multiplying to get the next step:

x^2+8x=x^2+5x+4

then simplify subtracting x^2 from both sides to get:

8x=5x+4

and next, subtract 5x from both sides to get:

3x=4

Finally divide both sides by 3 to get:

x=4/3.

As always, substitute back into the original to check the value:
(4/3)/((4/3)+4) = ((4/3)+1)/((4/3)+8)

Another method would be to graph x^2+8x and x^2+5x+4 and find out 
where the graphs cross.  This will be the solution point where the 
x-coordinate is 4/3.

-Doctor Chaos,  The Math Forum