Express (16x^2 + 4x^3)/(x^3 + 2x^2 - 8x) + 12x/(x-2) as one fraction in its simplest form.

Answer: 16x/(x - 2)

Start with the numerator of the first fraction, 16x2 + 4x3 , take a factor of 4x2 out to get 4x2(4 + x). Then look at the denominator of the fraction, x3 + 2x2 - 8x, immediately you can take out a factor of x to get, x(x2 + 2x - 8) which you can then factorise to get x(x - 2)(x + 4). From this you can see that x(x + 4) can be removed from the numerator and denominator to leave 4x/(x - 2). Then since the two fractions now have the same denominator you can just add the numerators together, 4x + 12x = 16x, giving the answer 16x/(x - 2).

Answered by Manon S. Maths tutor

3081 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Let f(x) = 5x^4 + 6x^3 + 3, find dy/dx at x = 3


The graphs of functions f(x)=e^x and h(x)=e^(-.5x), where x is a real number and 0<x<1 ,lie on a plane. Draw these functions and find the area they and the line x=0.6 enclose using integration correct to 3 decimal places


What is the angle between the position vectors a and b, where a = (6i - j + 3k) and b = (-4i + 2j + 10k)?


Given that y=(4x^2)lnx, find f"(x) when x=e^2


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