SOLUTION: I'm trying to rationalize the denominator of this of this equation x^2+x/sqrt(5x)+x Thank you and happy new year!!!

Algebra ->  Rational-functions -> SOLUTION: I'm trying to rationalize the denominator of this of this equation x^2+x/sqrt(5x)+x Thank you and happy new year!!!      Log On


   

Question 252914: I'm trying to rationalize the denominator of this of this equation
x^2+x/sqrt(5x)+x
Thank you and happy new year!!!
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
The equation i think is this:
%28x%5E2%2Bx%29%2F%28sqrt%285x%29%2Bx%29
step 1: to rationalize we multiply by a conjugate: sqrt(5x) - x in both numerator and denominator as:
%28x%5E2%2Bx%29%2F%28sqrt%285x%29%2Bx%29 * %28sqrt%285x%29-x%29+%2F+%28sqrt%285x%29+-+x%29
By foil we get
X%5E2%2Asqrt%285x%29+-+x%5E3+%2B+x%2Asqrt%285x%29+-+x%5E2 / 5x+-+x%5E2
Now, notice we can factor our, or cancel an x from everything. So, we get
X%2Asqrt%285x%29+-+x%5E2+%2B+sqrt%285x%29+-+x / 5+-+x