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

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

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Question 174274: Simplify:
matrix%281%2C3%2Csqrt%28x%29%2F%28sqrt%28x%29-3%29%2C+%27%2B%27%2C+5%2Fsqrt%28x%29%29
Thank you.

Answer by Edwin McCravy(6935) 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+%27%2B%27%2C+5%2Fsqrt%28x%29%29

The matrix%281%2C3%2CLCD%2C+%27=%27%2C+sqrt%28x%29%28sqrt%28x%29-3%29%29

matrix%281%2C3%2C%28sqrt%28x%29sqrt%28x%29%29%2F%28%28sqrt%28x%29-3%29sqrt%28x%29%29%2C+%27%2B%27%2C+%285%28sqrt%28x%29-3%29%29%2F%28sqrt%28x%29%28sqrt%28x%29-3%29%29%29

Multiply out the tops:

matrix%281%2C3%2Cx%2F%28%28sqrt%28x%29-3%29sqrt%28x%29%29%2C+%27%2B%27%2C+%285sqrt%28x%29-15%29%2F%28sqrt%28x%29%28sqrt%28x%29-3%29%29%29

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

%28+%28x%2B5sqrt%28x%29-15%29+%28x%2B3sqrt%28x%29%29%29+%2F%28+%28x-3sqrt%28x%29%29%28x%2B3sqrt%28x%29%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