Make x the subject of the equation y = {2(1+x)}/(3x+1)

This is an A* grade extension GCSE maths question on rearranging equations.

The question is asking us to find an equation that would represent x. In the question this x appears on the denominator (bottom half) and numerator (upper half). So the first thing we have to do is multiply out by the denominators to get rid of them. Lets do this one by one.

This gives:

y(3x-1) = 2(1+x)

To simplify the equation, we expand (multiply out) the bracket on the right hand side (RHS). Which gives us:

y (3x - 1) = 2 + 2x

Now we do the same thing to the left hand side (LHS):

3yx - y = 2 + 2x

Now, since we want x by itself, it is better to group x all together. So, we want to have the everything with x on the LHS and everything without an x on the RHS.

To do this, we'll have to add y to both sides and take away 2x on both sides to the above equation. 

3yx - y + y - 2x = 2 + 2x + y - 2x

As you can see, the positive and negatives will cancel and so this will give us:

3yx - 2x = y + 2

Excellent. Now we've made everything a lot simpler and makes it easy to answer the question. As you can see, x on the LHS is the common factor. So if we take out the x on the LHS like: 

x(3y - 2) = y + 2

we can see that to get x by itself, we will then need to divide both sides by 3y - 2 like so:

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

As you can see the (3y - 2) on the LHS will cancel and so this will give us:

x = (y + 2)/(3y - 2)

And there you have it!

Katrina G. GCSE Chemistry tutor, A Level Chemistry tutor, GCSE Maths ...

9 months ago

Answered by Katrina, a GCSE Maths tutor with MyTutor

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


£18 /hr

Raquel L.

Degree: Physics with Theoretical Physics (Masters) - Kings, London University

Subjects offered: Maths, Spanish+ 1 more


“I am a Physics with Theoretical Physics student at King´s College London. And if there is something that I love even more than Physics and Science is learning. I love it so much that I decided to leave my country, leaving there my fam...”

£30 /hr

Henri F.

Degree: Aerospace Engineering MEng (Masters) - Bristol University

Subjects offered: Maths, Physics+ 4 more

Further Mathematics

“About Me I am an Aerospace Engineer currently studying my MEng at the University of Bristol. I have always been fascinated with space, spacecraft and satellites. I intend on going on to complete a PhD specialising inSpacecraft Control...”

£18 /hr

Laura C.

Degree: Chemistry (Masters) - Durham University

Subjects offered: Maths, Science+ 3 more

-Personal Statements-

“Hello, I'm Laura. I know how hard GCSEs and A Levels are and the stress they can cause. I also know how beneficial having a friendly undestanding person to help can be. For me, that was my sister. For you, I hope that can be me.  I'm...”

About the author

£18 /hr

Katrina G.

Degree: Biochemical Engineering (Masters) - University College London University

Subjects offered: Maths, Science+ 1 more


“About Me: I am a Biochemical Engineering student at University College London (UCL). I have always had a real passion and love for all things 'science' and 'maths'  and hope that my tutorials will instill that love in you, too. I am v...”

MyTutor guarantee

You may also like...

Other GCSE Maths questions

Solve the simultaneous equations 4x + 7y = 1 and 3x +10y = 15.

Rearrange the formula to make 'y' the subject: x = (1 - 2y)/(3 +4y)

How do you work out the length of one of the sides of a right-angled triangle given the other two?

Can you run through the quadratic equation(including the sketch and algebra).

View GCSE Maths tutors


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