How to solve an equation when the variable is in the denominator?

I find the best way to explain maths is by using more numbers than words, so I'll use an example to explain this:

3 - 2x+2/x+4 = 4

A good thing to do before attempting to solve an equation is to get rid of any denominators you have, in this case x+4

To do this we can multiply the fraction (2x+2/x+4) by (x+4) and both (x+4) would cancel each other out, leaving us with 2x+2!

However, this is an equation, which means that anything you change to one side of the = sign you have to do the same on the other side, to keep everything equal and balanced.

Another important thing to remember is that we will be multiplying (x+4) not x and 4, so I find it easier to put some brackets around them so we don't forget what we're doing. Now enough words, let's use the numbers to demonstrate what I mean:

3 - 2x+2/x+4 = 4

(x+4) x 3  +  (x+4) x -(2x+2/x+4)  =  (x+4) x 4

3x + 12 - (2x + 2) = 4x + 16

3x + 12 - 2x - 2 = 4x + 16

x + 10 = 4x + 16

x - 4x = 16 - 10

-3x = 6

x = -2

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