How to express (4x)/(x^2-9)-2/(x+3)as a single fraction in its simplest form.

First we should be aware of the relationship bewteen the denominator of the two fractions. Since x^2-9=(x+3)(x-3), we can multiply (x-3) on both numerator and denominator of the fraction of 2/(x+3). Hence the fraction becomes 2(x-3)/(x+3)(x-3)=2(x-3)/(x^2-9). Therefore now we can substract it from the first fraction, becomes (4x)/(x^2-9)-2(x-3)/(x^2-9). Since the denominator is the same, so we can substact the numerator straightaway. And the next step will be [4x-2(x-3)]/(x^2-9)=(2x-6)/(x^2-9)=2(x-3)/(x^2-9). Be aware here that (x^2-9) can be split into (x+3)(x-3). This is a very common mistake. Hence devide (x-3) from both denominator and numerator and final answer will be 2/x+3.

Answered by Kexin Y. Maths tutor

3874 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The point A lies on the curve with equation y = x^(1/2). The tangent to this curve at A is parallel to the line 3y-2x=1. Find an equation of this tangent at A. (PP JUNE 2015 AQA)  


Find the constant term in the expression (x^2-1/x)^9


a) Express 4(cosec^2(2x)) - (cosec^2(x)) in terms of sin(x) and cos (x) and hence b) show that 4(cosec^2(2x)) - (cosec^2(x)) = sec^2(x)


A ball is projected at an angle b from the horizontal. With initial velocity V the ball leaves the ground at point O and hits the ground at point A. If Vcos(b) = 6u and Vsin(b) = 2.5u, how long does the ball take to travel between O and A.


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