Question

Which choice is equivalent to the fraction below when x is an appropriate

value? Hint: Rationalize the denominator and simplify.
5
5+√102

Answer 1

Explanation:

To simplify the fraction 5/(5+√102), we can rationalize the denominator by multiplying the numerator and the denominator by the conjugate of the denominator, which is 5-√102.

So, we get:

5/(5+√102) * (5-√102)/(5-√102) = (5(5-√102))/(25-102)

Simplifying the denominator by combining 25 and -102, we get:

(5(5-√102))/(-77)

Now, we can simplify the expression by dividing both the numerator and the denominator by -1 to obtain:

-5(√102-5)/77

Therefore, an equivalent choice is:

-5(√102-5)/77