Simplify (3x^2 + x -2)/(x^2 - 1)

First notice that no simplifications can be made to the problem without changing the form. We start by factorising the numerator. The highest power of x in this question is 2, therefore we know that it has to be a quadratic. The general form of a quadratic is Ax2+Bx+C. We need to find 2 factors of -2 that add up to 1 when one of the factors is multiplied by 3 (as A = 3). The possible factors are -1 and 2 or -2 and 1. Start with -1 and 2. The two possibilities are: 1) (3x - 1)(x + 2)- the sum of the coefficients of x is 5. 2) (3x + 2)(x - 1) - the sum of the coefficients of x is -1Then try -2 and 1. The two possibilities are: 1) (3x + 1)(x - 2) - the sum of the coefficients of x is -5. 2) (3x - 2)(x + 1) - the sum of the coefficients of x is 1.Therefore the factorised form is (3x - 2)(x + 1).The denominator can then be simplified very easily by noticing that x2 -1 is in the form a2-b2. We know that a2-b2 = (a+b)(a-b). Applying this to the denominator gives (x+1)(x-1). To simplify (3x2 + x -2)/(x2 - 1) we rewrite it in the form [(3x - 2)(x + 1)/(x + 1)(x - 1)] and cancel x + 1 giving the simplified form as (3x - 2)/(x - 1).

Answered by Arjun A. Maths tutor

3536 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

In a sale, normal prices are reduced by 18%. The sale price of an umbrella is £25.83. Work out the normal price of the umbrella.


A lorry can travel 35 miles per litre of diesel that costs £7.30 per litre. What is the cost in £ (to the nearest 2 decimal places) of the diesel used in driving the lorry 200 miles?


Prove that the multiple of an even number and an odd number is always even.


Expand and simplify (2x+4)(x+2)


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences