Simplify (7+sqrt(5))/(sqrt(5)-1), leaving the answer in the form a+b*sqrt(5)

Step 1 - Identify the difference between the required form of the answer and the expression to be simplified: 

It can be seen that in order to simplify the expression we need to somehow get rid of the denominator.

Step 2 - Attempt a method to get rid of the denominator: 

The best way to get rid of the denominator is to multiply it by (sqrt(5)+1). In order to keep the expression the same we must do the same to the numerator as well. 

This gives us,

((7+sqrt(5))/(sqrt(5)-1))*((sqrt(5)+1)/(sqrt(5)+1))

Step 3 - Carry out the necessary calculations:

The top parts of the fractions multiply together and the bottom parts of the fractions multiply together.

For the top part this gives us,

(7+sqrt(5))(sqrt(5)+1) = 7sqrt(5)+7+5+sqrt(5)

= 8*sqrt(5)+12

For the bottom part this gives us,

(sqrt(5)-1)*(sqrt(5)+1) = 5+sqrt(5)-sqrt(5)-1 = 4

Dividing the top part by the bottom part gives us,

2*sqrt(5)+3

Step 4 - Check that the answer is in the correct form.

The question asks for an answer in the form,

a+b*sqrt(5)

Our answer can be written in this format with a = 3 and b = 2.

Answered by Ian R. Maths tutor

19356 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Express X/((X+1)(X+2)) in partial fractions. OCR C4 style question


Prove algebraically that n^3 +3n -1 is odd for all positive integers n


The curve y = 4x^2 + a/ x + 5 has a stationary point. Find the value of the positive constant a given that y-ordinate of the stationary point is 32.


Find the values of k for which the equation (2k-3)x^2-kx+(k-1) has equal roots


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences