MYTUTOR SUBJECT ANSWERS

731 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...

9 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

295 SUBJECT SPECIALISTS

£26 /hr

Chloe W.

Degree: Mathematics (Bachelors) - Bristol University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“About Me:I'm Chloe and I'm a 2nd year maths student at Bristol university. I've always enjoyed working with numbers and I hope that I can encourage others to love working with them too!I've tutored both of my siblings through their...”

£20 /hr

James A.

Degree: Mechanical Engineering (Masters) - Southampton University

Subjects offered:Maths, Physics

Maths
Physics

“I am a Mechanical Engineering Student at the University of Southampton specialising in tutoring maths and physics to a thorough standard.”

MyTutor guarantee

£20 /hr

Joshua D.

Degree: Economics and Mathematics (Bachelors) - Bath University

Subjects offered:Maths, Science+ 2 more

Maths
Science
Physics
Economics

“Enthusiastic tutor from the University of Bath, aiming to push pupils to achieve the best that they can.”

About the author

£30 /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

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

How do you find the minimum of the equation sin^2(x) + 4sin(x)?

Why do we need to differentiate?

How and when do you use integration by parts?

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