Express 3/2x+3 – 1/2x-3 + 6/4x^2-9 as a single fraction in its simplest form.

First it is necessary to notice that 4x^2-9 can be written as (2x-3)(2x+3). To solve this question, you first have to write all the fractions in terms of their lowest common denominator. In this case that is (2x+3)(2x-3). Therefore you have to multiply 3/2x+3 by 2x-3/2x-3 and 1/2x-3 by 2x+3/2x+3. This will leave you with 3(2x-3)-1(2x+3)+6/(2x-3)(2x+3). If you multiply this out you are left with 4x-6/(2x-3)(2x+3). 4x-6 can be rewritten as 2(2x-3), and therefore the 2x-3s cancel out leaving 2/2x+3 which is the final answer.

Answered by Dhian S. Maths tutor

11871 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How can you find out if two lines expressed in their vector form intersect?


A girl saves money over 200 weeks. She saves 5p in Week 1, 7p in Week 2, 9p in Week 3, and so on until Week 200. Her weekly savings form an arithmetic sequence. Find the amount she saves in Week 200. Calculate total savings over the 200 week period.


If f(x) = (3x-2) / x-5 x>6, find a.) ff(8) b.) the range of f(x) c.) f^-1(x) and state its range.


Solve the equation |3x +4a| = 5a where a is a positive constant.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences