SOLUTION: Simplify: {{{matrix(1,3,sqrt(x)/(sqrt(x)-3), "+", 5/sqrt(x))}}} Thank you.

Algebra ->  Radicals -> SOLUTION: Simplify: {{{matrix(1,3,sqrt(x)/(sqrt(x)-3), "+", 5/sqrt(x))}}} Thank you.       Log On


   

Question 174274: Simplify:
matrix%281%2C3%2Csqrt%28x%29%2F%28sqrt%28x%29-3%29%2C+%22%2B%22%2C+5%2Fsqrt%28x%29%29
Thank you.

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

matrix%281%2C3%2Csqrt%28x%29%2F%28sqrt%28x%29-3%29%2C+%22%2B%22%2C+5%2Fsqrt%28x%29%29

The matrix%281%2C3%2CLCD%2C+%22=%22%2C+sqrt%28x%29%28sqrt%28x%29-3%29%29



Multiply out the tops:



Combine the tops over the LCD:

%28x%2B5sqrt%28x%29-15%29%2F%28sqrt%28x%29%28sqrt%28x%29-3%29%29

Multiply out the bottom

%28x%2B5sqrt%28x%29-15%29%2F%28x-3sqrt%28x%29%29

Put top and bottom in parentheses:

%28%28x%2B5sqrt%28x%29-15%29%29%2F%28%28x-3sqrt%28x%29%29%29

To rationalize the denominator, multiply
top and bottom by %28x%2B3sqrt%28x%29%29



%28x%5E2%2B3x%2Asqrt%28x%29%2B5x%2Asqrt%28x%29%2B15x-15x-45sqrt%28x%29%29%2F%28x%5E2-9x%29

%28x%5E2%2B8x%2Asqrt%28x%29-45sqrt%28x%29%29%2F%28x%5E2-9x%29

Edwin