Solve the equation (2x+3)/(x-4)-(2x-8)/(2x+1)=1 and give the answer to 2 decimal places

To start off with we need to remove the two denominators (the bottom part of the fractions) on the left hand side of the equation. This can be achieved by multiplying the through the whole equation by (x-4)(2x+1), since (x-4)/(x-4)=1 and (2x+1)/(2x+1)=1. This procedure transforms the equation into the following:


Now we continue by multiplying out the brackets, which gives:


Which simplifies to:

24x-29=-7x-4 (remember when subtracting the left hand side, that minus a minus number is a plus. Also note that we want to add and subtract according to the power of the x variable i.e. the x^2 needs to be in a separate grouping to the x^1 and x^0).

Continue with the equation by adding 7x to each side of the equality and adding 29 to each side. This yields the following:


Now to get the solution for the variable x, we divide both sides by 31 and this gives:


Inputting this fraction into the calculator gives the decimal solution as:


The question asks for the answer to be to decimal places and so the answer is:


Overview: This is hard question for a GCSEs maths student and is in the A* ability criteria, but the through some simple techniques/ steps, the question is a lot more manageable and solvable.

A breakdown of the steps:

1. Multiply the whole of the equation by the product of the denominators of the fractions. There by eliminating the denominators.

2. Expand the brackets with care.

3. Group the correct coefficients when adding/subtracting {i.e. keeping the powers of x together).

4. Once the coefficients have been grouped together successfully, then manipulate the equation by subtracting/adding on each side to get x equal to a number.

5. Remember to put the answer in the form wanted by the question. If it does not state the form wanted then put it into 2 decimal places to be safe.

Jake J. GCSE Maths tutor

1 year ago

Answered by Jake, a GCSE Maths tutor with MyTutor

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


£18 /hr

Mia V.

Degree: Chemistry (Masters) - Durham University

Subjects offered: Maths, Physics+ 1 more


“I am a Chemistry student at Durham University. I've always had a passion for learning new things, but most importantly helping others to learn new things too! I'm an open, patient individual who aims to put you at ease with your scien...”

£18 /hr

Ann L.

Degree: Dentistry (Bachelors) - Birmingham University

Subjects offered: Maths, Chemistry+ 3 more

-Personal Statements-

“I'm Ann, a dental student, and I want you to succeed in your education. As a student ambassador for my university, and a past volunteer tutor at a local secondary school, I'm experienced in working with young people and inspiring you ...”

£18 /hr

Wesley M.

Degree: Mathematics (Masters) - Bristol University

Subjects offered: Maths, Physics+ 1 more


“I am a current Mathematics student at The University of Bristol. Maths can be a love-hate sort of subject for many people, but with my absolute love and enthusiasm for both maths itself and the idea of inspiring others, I hope to be a...”

About the author

£18 /hr

Jake J.

Degree: Mathematics and its applications (Bachelors) - Cardiff University

Subjects offered: Maths


“Background:I am a Maths student currently studying at Cardiff University. I have experience giving tuitionto several GCSE students prior to their exams. Through this experience I have learnt techniques to help learn Math concepts tha...”

MyTutor guarantee

You may also like...

Posts by Jake

Find the highest common factor (HCF) of 12 and 18.

Solve the equation (2x+3)/(x-4)-(2x-8)/(2x+1)=1 and give the answer to 2 decimal places

Other GCSE Maths questions

s^2 - 2s - 24 = 0

How do I make calculations with percentages?

How do I know when a quadratic function crosses the y-axis?

Solve the equation 3x squared + 4x – 12 = 0 Give your solutions correct to 2 decimal places.

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