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.

DS
Answered by Dhian S. Maths tutor

12403 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

If the functions f and g are defined: f: x--> x/5 + 4 g : x--> 30x + 10. what is x, if fg(x) = x. ?? What would fgf(x) = x^2 be??


Find the total area enclosed between y = x^3 - x, the x axis and the lines x = 1 and x= -1 . (Why do i get 0 as an answer?)


Find the integral of 4x^2 - 10x + 1/(x^(1/2)), with respect to x, in its simplest form.


Find the equation of the straight line tangent to the curve y=2x^3+3x^2-4x+7, at the point x=-2.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning