Simplify the algebraic expression: (3x^2-7x-6)/(x^2-6x+9)

We start by noticing that both the numerator and denominator are expressions which can be factorised into brackets. Starting with the numerator, we multiply the coefficient of x^2 and the constant term together (3 x -6 = -18). We then look for factors of -18 which add up to -7. We find 2 and -9, so we rewrite the numerator as 3x^2+2x-9x-6. We then look for common factors between the x^2 and x terms. We find 3x from 3x^2 and 9x. We combine and factorise these two terms and then do the same with the remaining terms. This gives us 3x(x-3)+2(x-3). We factorise the (x-3) out and this gives us (3x+2)(x-3). We use the same method to factorise the denominator which leaves us with (3x+2)(x-3)/(x-3)^2. We cancel out (x-3) and obtain the final answer (3x+2)/(x-3).

EG
Answered by Emily G. Maths tutor

3739 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

A plane flew from Frankfurt to Hong Kong. The flight time was 10hours 45minutes. The average speed was 852km/h. Work out the distance the plane flew.


factorise 2x^2 - x - 6


Solve the equation: (2x+3)/(x-4)-(2x-8)/(2x+1)=1


Find the value of X when 3x^2 + 6x + 3 = 0


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