Algebra help- rationalizing the denominator

Question

Good evening,

 

I am in need of assistance working through this problem. It is an example in my text book, so it lists out the steps. The problem is that I ended up at the second to last step, which it says to use the distrubutive property to get the answer. I am really stumped as to how they got it. I have been able to simplify all of the others, but this one has me confused. 

 

The original example is 4/1+SR5. (SR is square root). I multiplied by the conjugate and ended up with 4-4SR5/-4. The book says the answer is SR5-1. Perhaps I've been looking at it too long to see the answer. 

 

Any assistance that can be provided is welcomed. Thank you. 

Answer 1

Megan,

You had (4 -4√5)/(-4).

The next step is simplifying. Each term in the numerator and the denominator has a factor 4. Moreover, you have a negative sign that you may be able to eliminate. Therefore, divide each term by the same factor,

 

(4 -4√5)/(-4)    Divide each term by (-4)

[4/(-4)  - (4√5)/(-4)]/(-4/-4)     Then simplify

= -1 +√5 OR

= √5 - 1

 

Answer 2

4 / (1+√5)                                 [we want to get rid of √ in the denominator]

(1-√5)4 / [(1-√5)(1+√5)]           [multiply by 1]

(1-√5)4 / [1 - 5]                         [  because (a² - b²⁾ = (a-b)(a+b) ]

(1-√5)4) / (-4)

√5 - 1

 

Now, take another look at your answer of:

(4-4√5) / (-4)                          [ parentheses are important here)

4(1-√5) / (-4)                          [ let's not distribute the 4; let's cancel it ]

 (-1)(1-√5)

  √5 - 1                                   [ seems like you had it right ]