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).

MS
Answered by Manon S. Maths tutor

3125 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Solve the inequality x < 4 - |2x + 1|.


How do you find the gradient of a line?


I don't understand how to visualise differentiation, please could you show my an example to allow me to understand what it actually is better?


I'm confused about differentiation and integration, could you explain these to me?


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