MYTUTOR SUBJECT ANSWERS

445 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

257 SUBJECT SPECIALISTS

£20 /hr

Dylan D.

Degree: Mathematics MMath (Masters) - Bath University

Subjects offered: Maths

Maths

“About me I'm studying Maths at the University of Bath. I really enjoy the subject, and genuinely love learning and talking about Maths- which often surprises some who don't appreciate it so much! -But if I can help inspire others to e...”

£24 /hr

Osian S.

Degree: Mathematics (Masters) - Warwick University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“Hi, I'm Osian, a Master's student at the University of Warwick. I've had fun with mathematics from a young age, and I hope to be able to instill this passion for mathematics in you, through my tutorials! Throughout my time at Warwick,...”

£20 /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...”

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 roots of the equation y=x^2-8x+5 by completing the square.

How do I find the equation of the normal line given a point on the curve?

How do I sketch a graph of a polynomial function?

How would I integrate the indefinite integral x^2 dx?

View A Level Maths tutors

Cookies:

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

mtw:mercury1:status:ok