Rationalize the numerator and simplify to the lowest term 4

Rationalize the numerator and simplify to the lowest term

4- sqrt(x)/x-16

Solution

[ 4 + sqrt(x) ]/(x -16)

To rationalise the numerator multiply the numerator and denominator with its conjugate

i.e. 4 - sqrtx

So, [ 4 + sqrt(x) ]/(x -16) = ( 4+ sqrtx)( 4 - sqrtx)/(x - 16)(4 - sqrtx)

= ( 16 -x)/( 4x -xsqrtx -64 +16sqrtx)

= (16 -x)/( -sqrtx(x- 16) + 4(x -16) )

= ( 16 -x) /(x-16)( 4 - sqrtx)

= 1/( 4 -sqrtx)