can someone help me with simplification: �ã20/5 - 1/�ã5

my first answer is 1/�ã5
my second answer is 10 -�ã5/5
but the answere I have to choose from are:
(a) �ã20 - 5�ã5/�ã5
(b) �ã20 - �ã5/5
(c) cannot be simplified
(d) 1/5�ã5
which is correct and if I'm not where did I go wrong?

�√20/5 - 1/�√5

= 2√5/5 - 1/√5*(√5/√5)
= 2√5/5 - √5/5
= √5/5

by the way:

1/√5 = √5/5 so your answer would be correct.
However, it is considered "better form" to have radicals in the denominator rationalized

To simplify the expression �√20/5 - 1/�√5, we can follow these steps:

Step 1: Rationalize the denominator of the second fraction by multiplying both numerator and denominator by √5. This is done to eliminate the radical in the denominator:

�√20/5 - 1/�√5 * (√5/√5) = �√20/5 - √5/5

Step 2: Find a common denominator for both fractions, which is 5 in this case. Multiply the numerator and denominator of the first fraction by √5:

(�√20 * √5)/(5 * √5) - √5/5 = (2√5 * √5)/(5 * √5) - √5/5

Simplifying the first fraction:

(2√5 * √5)/(5 * √5) = (2 * √5 * √5)/(5 * √5) = 2(√5 * √5)/(5 * √5) = 2(√5 * √5)/(5 * √5 * √5) = 2(√5)/(5 * √5) = (2/5)

The expression becomes:

(2/5) - √5/5

Step 3: Combine the fractions with a common denominator:

(2/5) - √5/5 = (2 - √5)/5

Therefore, the simplified expression is (2 - √5)/5.

Now, let's compare the simplified expression with the answer choices:

(a) �√20 - 5�√5/�√5 - This is not equivalent to the simplified expression.
(b) �√20 - �√5/5 - This is not equivalent to the simplified expression.
(c) cannot be simplified - This is incorrect because the expression can be simplified.
(d) 1/5�√5 - This is not equivalent to the simplified expression.

From the provided answer choices, none matches the simplified expression. However, your initial answer of √5/5 is correct. Keep in mind that when dealing with radicals, it is often preferred to rationalize the denominator, which means eliminating any radicals in the denominator. In this case, rationalizing the denominator would leave us with √5/5, which is equivalent to the simplified expression (2 - √5)/5.