Rationalize the numerator.
((√a) -2)/(a-4)
( √a - 2 ) / ( a - 4 )
Multiply by the conjugate ( √a + 2 ) / ( √a + 2 )
( √a - 2 ) / ( a - 4 ) = ( √a - 2 ) ( √a + 2 ) / [ ( a - 4 ) ( √a + 2 ) ]
Difference of square formula:
x² - y² = ( x - y ) ( x + y )
So:
( √a - 2 ) ( √a + 2 ) = a - 4
( √a - 2 ) / ( a - 4 ) = ( a - 4 ) / [ ( a - 4 ) ( √a + 2 ) ] =
1 / ( √a + 2 )
--- OR ---
a - 4 = ( √a )² - 2²
Difference of square formula:
x² - y² = ( x - y ) ( x + y )
( √a )² - 2² = ( √a - 2 ) ( √a + 2 )
a - 4 = ( √a - 2 ) ( √a + 2 )
So:
( √a - 2 ) / ( a - 4 ) = ( √a - 2 ) / [ ( √a - 2 ) ( √a + 2 ) ] = 1 / ( √a + 2 )