how do you simplify by rationalizing the denominator in this equation?

Question

radical 11 - radical 5/ radical 11 + radical 5

Answer 1

Solve the expressions....

(V`11 - V`5)/(V`11 + V`5)

First: multiply the denominator's conjugate (opposite sign) with the denominator & numerator.

(V`11 - V`5)(V`11 - V`5)/(V`11 + V`5)(V`11 - V`5)

Sec: eliminate parenthesis by using the Foil Method & you should get...

(V`121-V`55-V`55+V`25)/(V`121-V`55+V`55+V`25)
(11- 2 V`55+5)/(11+5)
(11 + 5 - 2 V`55)/16
(16 - 2 V`55)/16

Third: separate the numerators by placing 16 & - 2V`5 over the denominator.

a. 16/16 - (2V`55)/16
16/16 - (2/16)V`55
1 - (1/8)V`55
1 - (V`55)/8

Answer 2

multiply top and bottom by radical 11 - radical 5 to rationalize the denominator and distribute on top.

Answer 3

Multiply the numerator and denominator by [sqrt(11) - sqrt(5)]. If you multiply the denominator by that expression, you get 6, an integer. Multiplying both the numerator and denominator means that you've effectively multiplied by 1, and therefore you haven't changed the value.

If the denominator of a fraction to be rationalized is sqrt(x) +/- sqrt(y), multiply the numerator and denominator by sqrt(x) -/+ sqrt(y), where you reverse the sign. This always gives you an integer denominator if x and y are integers, because the new denominator will be equal to x - y.