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

Gabriela D. GCSE Maths tutor, GCSE Chemistry tutor, 13 plus  Portugue...

3 years ago

Answered by G, who tutored GCSE Maths with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


PremiumIgnacio P. GCSE Business Studies tutor, IB Spanish tutor, A Level Spa...
£36 /hr

Ignacio P.

Degree: Aerospace Engineering MEng (Masters) - Bristol University

Subjects offered:Maths, Spanish+ 5 more

Further Mathematics
-Personal Statements-

“Author of The 3-Step Method to Achieving (under publishing) - APPLIED NEUROSCIENCE & COACHING FOR EXPLOSIVE RESULTS IN MATH, PHYSICS, SPANISH & MORE!”

£20 /hr

Xanthe W.

Degree: Biological Sciences with a Year in Industry/Research (Bachelors) - Imperial College London University

Subjects offered:Maths, Chemistry+ 1 more


“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

£20 /hr

Lucy S.

Degree: Chemistry (Masters) - Durham University

Subjects offered:Maths, Chemistry


“Reading Chemistry at Durham University with expertise in Chemistry and Mathematics (A*A*) at GCSE/A-level”

About the author

G D.

Currently unavailable: no new students

Degree: Medicine (Bachelors) - Southampton University

Subjects offered:Maths, Chemistry


“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

How would I solve x^2 + 7x + 10 = 0

Solve the equation 3x^(2)-7x+3 giving your answer to three significant figures.

How do I find the equation of a straight line?

Solve the simultaneous equations: 5x + 3y = 9 and 7x - 2y = 25.

View GCSE Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss