SOLUTION: Rationalize the denominator assume all expressions under radicals represent positive numbers.
(2-√y)/(3+√y) please help, I have trouble with these
Thank you
Algebra ->
Polynomials-and-rational-expressions
-> SOLUTION: Rationalize the denominator assume all expressions under radicals represent positive numbers.
(2-√y)/(3+√y) please help, I have trouble with these
Thank you
Log On
Question 274592: Rationalize the denominator assume all expressions under radicals represent positive numbers.
(2-√y)/(3+√y) please help, I have trouble with these
Thank you
You can put this solution on YOUR website! (2-√y)/(3+√y)
To eliminate a radical in the denominator we can multiply both the numerator and denominator by the "conjugate" of the denominator. This is the same a multiplying by 1 so the value of the expression is not changed by doing this. In this case the conjugate of 3+sqrt(y) is 3-sqrt(y) so we have:
[(2-sqrt(y)*(3-sqrt(y)]/[(3+sqrt(y)*(3-sqrt(y))]
Using FOIL above the numerator becomes:
2*3 - 2*sqrt(y) - 3*sqrt(y) + sqrt(y)*sqrt(y) =
6 - 5*sqrt(y) + sqrt(y*y) =
6 - 5*sqrt(y) + y
The denominator becomes:
3*3 - 3 sqrt(y) + 3*sqrt(y) - sqrt(y)*sqrt(y) =
9 - sqrt(y*y) =
9 - y
Putting numerator and denominator together then we have:
(6 - 5*sqrt(y) + y)/(9 - y)
You can put this solution on YOUR website! Rationalize the denominator assume all expressions under radicals represent positive numbers.
(2-√y)/(3+√y) please help, I have trouble with these
------------------
Always multiply by the conjugate of the DEN. In this case it's
-------------------
That gives you:
Then multiply the NUM
=
(
