MYTUTOR SUBJECT ANSWERS

557 views

C1 - Simplifying a fraction that has a root on the denominator

(7+√5)/(√5-1) 

In this example we are given (√5-1) as our denominator, and we want to simplify this complex fraction into the form a + b√5. 

In order to do this our first step is to elimate the denominator. To do this, we use the rule associated with the Difference of Two Squares. For example, if you were told to factorise and simplify: x 2 - 16, you would get (x-4)(x+4) since when you expand the '-4x' and '+4x' would cancel each other out to leave x2 - 16. 

To return to our question therefore, we need to multiply our fraction by something to eliminate the √5 on the denominator. This something is (√5 +1) as the opposite signs will mean the middle part of our expanded equation +√5-√5 will cancel each other out, and multiplying √5 by itself will eliminate the square root. But we must remember, that whatever we do to the bottom of the fraction we must also do to the top, therefore we must multiply both the numerator and the denominator by (√5 + 1)

So:  (7+√5)/(√5-1) x (√5+1)/(√5+1)

Multiplying the numerators (top of the fractions) together, we get: (7x√5) + (7x1) + (√5x√5) + (√5x1), which equals: 7√5 + 7 + 5 + √5    

By collecting like terms this simplifies to: 8√5 + 12

Multiplying the denominators (bottom of the fractions) together, we get: (√5x√5) + (√5x1) - (1x√5) - (1x1)     which equals: 5 + √5 - √5 - 1      

Again, by collecting like terms this simplifies to: 4

Therefore, we can also write (7+√5)/(√5-1) as:

(8√5 + 12) / 4

But this can be simplified further as both 8, and 12 are divisible by 4, and therefore this can finally be written as: 

2√5 + 3     or     3 + 2√5

SOLUTION:     a = 3      and      b = 2

Claudia M. GCSE Maths tutor, A Level Maths tutor, A Level Economics t...

1 year ago

Answered by Claudia, who has applied to tutor A Level Maths with MyTutor


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

265 SUBJECT SPECIALISTS

Ethan R. A Level Maths tutor, GCSE Maths tutor
£20 /hr

Ethan R.

Degree: Maths and Physics (Masters) - Durham University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Hi, I'm Ethan. I like to take a friendly approach to tutoring and want to learn what works best for you. Maths can be easy, as long as you know how!”

Timothy N. A Level Design & Technology tutor, GCSE Design & Technolog...
£20 /hr

Timothy N.

Degree: Architecture and Environmental Engineering (Masters) - Nottingham University

Subjects offered:Maths, Science+ 3 more

Maths
Science
Physics
Design & Technology
-Personal Statements-

“Hi there, I have a passion for helping students achieve, and believe that with my years of experience tutoring, we will be able to surpass the grades you want!”

£20 /hr

Sophie H.

Degree: Mathematics (Masters) - Bristol University

Subjects offered:Maths

Maths

“I’ll help anyone finding maths hard. I still struggle now, it's not meant to be easy! Be at my tutorial or (c^2-a^2) <- a maths joke, I apologise.”

About the author

£20 /hr

Claudia M.

Degree: Economics (Bachelors) - Durham University

Subjects offered:Maths, Economics

Maths
Economics

“About Me:Hi! I am an economics student at Durham University, whom understands that our economy is volatile and unpredictable, which can make understanding how it works particularly difficult at times. However, so long as we underst...”

MyTutor guarantee

You may also like...

Other A Level Maths questions

Find the shortest distance between the line L: x=1+t, y=1+2t, z=1-t and the point A: (2,3,4)

Explain briefly the Normal Distribution

How do I integrate sin^2 (x) dx?

Write down two reasons for using statistical models

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