rationalize the denominator in the following radicals and collect the like terms
12/ 3-√5
To rationalize the denominator, we will multiply both the numerator and the denominator by the conjugate of the denominator, which is 3+√5.
(12/(3-√5)) * ((3+√5)/(3+√5))
Expanding the numerator and the denominator using the distributive property:
= (12 * 3 + 12 * √5) / (3 * 3 + 3 * √5 - 3 * √5 - √5 * √5)
Simplifying:
= (36 + 12√5) / (9 - 5)
= (36 + 12√5) / 4
Now, we can simplify further by dividing both the numerator and the denominator by 4:
= (9 + 3√5) / 1
= 9 + 3√5
So, the rationalized form of the expression is 9 + 3√5.