MYTUTOR SUBJECT ANSWERS

968 views

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

This is an algebraic fraction. There is more than one way of solving this expression, but the simplest is to factorise both the top and the bottom quadratic expressions.

Firstly we shall simplify the top expression, 3x^2-x-2. This means putting it in the form (ax + b)(cx + d) where a, b, c, and d are constants. 

Now, the only way to get 3x^2, you can see that a multipled by c must equal to 3. Therefore, (3x + b)(x + d). Now you can also see that b multiplied by d must be -2, but also, 3 multipled by d plus b multiplied by x must also be -1. Therefore it can be seen that b is 2, and d is -1. So now the top is (3x + 2)(x -1).

Next, we factorise the bottom of the fraction. At first glance, it looks like it is the simplest it can be. However, x^2 - 1 is actually the difference of two squares. This is (x + 1)(x - 1).

Now, the full factorised expression becomes (3x + 2)(x - 1)/(x + 1)(x - 1). As (x - 1) is on the top and the bottom, this is equal to 1, and can be cancelled out.

So now we have the answer! (3x + 2)/(x + 1)

Venetia L. A Level Maths tutor, GCSE Maths tutor, A Level Further Mat...

11 months ago

Answered by Venetia, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

257 SUBJECT SPECIALISTS

Sahil M. A Level Biology tutor, GCSE Biology tutor, A Level Chemistry...
£22 /hr

Sahil M.

Degree: Medicine (Bachelors) - Manchester University

Subjects offered:Maths, Spanish+ 3 more

Maths
Spanish
Chemistry
Biology
-Medical School Preparation-

“Hello! My name is Sahil and I am currently a medical student at the University of Manchester. I am really looking forward to tutoring you in Spanish, Chemistry, Biology or Maths as well as trying to help you during the difficult proce...”

£20 /hr

Daniel O.

Degree: Natural Sciences (Masters) - Nottingham University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Chemistry

“An enthusiastic Natural Sciences undergraduate at the University of Nottingham with industry experience working for the Defence Science Technology Laboratories.”

£20 /hr

Madeleine N.

Degree: Maths and Physics (Masters) - Durham University

Subjects offered:Maths, Spanish+ 2 more

Maths
Spanish
Physics
Further Mathematics

“Enthusiastic student, studying Maths and Physics at Durham university: keen to work hard with students to improve their results.”

About the author

£36 /hr

Venetia L.

Degree: General Engineering (Masters) - Durham University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I study General Engineering at the University of Durham. I have always enjoyed maths and sciences, so hope to help students who share my love for them too!”

You may also like...

Posts by Venetia

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

Solve 5x + 4 = 14 + x

The equation of a curve is y = x^2 - 5x. Work out dy/dx

Other A Level Maths questions

How can we solve a two-equation, two-unknown values?

How do I differentiate y=(4+9x)^5 with respect to x?

Solve for 0<=θ<π, the equation sin3θ-(sqrt3)cosθ=0 (C2)

Find the first differential with respect to x of y=tan(x)

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok