Question 174274
<pre><font size = 4 color = "indigo"><b>
{{{matrix(1,3,sqrt(x)/(sqrt(x)-3), "+", 5/sqrt(x))}}}

The {{{matrix(1,3,LCD, "=", sqrt(x)(sqrt(x)-3))}}}

{{{matrix(1,3,(sqrt(x)sqrt(x))/((sqrt(x)-3)sqrt(x)), "+", (5(sqrt(x)-3))/(sqrt(x)(sqrt(x)-3)))}}}

Multiply out the tops:

{{{matrix(1,3,x/((sqrt(x)-3)sqrt(x)), "+", (5sqrt(x)-15)/(sqrt(x)(sqrt(x)-3)))}}}

Combine the tops over the LCD:

{{{(x+5sqrt(x)-15)/(sqrt(x)(sqrt(x)-3))}}}

Multiply out the bottom

{{{(x+5sqrt(x)-15)/(x-3sqrt(x))}}}

Put top and bottom in parentheses:

{{{((x+5sqrt(x)-15))/((x-3sqrt(x)))}}}

To rationalize the denominator, multiply
top and bottom by {{{(x+3sqrt(x))}}}

{{{( (x+5sqrt(x)-15) (x+3sqrt(x))) /( (x-3sqrt(x))(x+3sqrt(x)) )}}}

{{{(x^2+3x*sqrt(x)+5x*sqrt(x)+15x-15x-45sqrt(x))/(x^2-9x)}}}

{{{(x^2+8x*sqrt(x)-45sqrt(x))/(x^2-9x)}}}

Edwin</pre>