Question

How would the fraction

using difference of squares?
be rewritten if its denominator is rationalized
1-√5

Answer 1

To rationalize the denominator of the fraction 1−V5

​, eliminate the radical in the denominator. This is done by multiplying the numerator and denominator by the conjugate of the denominator.

​(1-V5)/1 *(1+V5)/(1+V5)

​​

Now let's apply the cross product rule:

(1-V5)(1+V5)/(1+V5)=(1-5)/(1+V5)= -4/1+V5

The denominator has been streamlined, and the fraction becomes:

-4/(1+V5)

This is the equivalent expression for the fraction difference 1-V5

​ with a rationalized denominator.

Explanation: