For the rational function with x 4 in the numerator and 2x

For the rational function with x – 4 in the numerator and 2x + 1 in the denominator, why is it alright for x to equal 4 but not equal 1/2? Explain

f(x) = ( x-4)/(2x+1)

if numerator is equal to zero: x-4 =0---> x =4

at thi point f(x) =0 , this the point where f(x) crosses the x axis and is known as zero of f(x)

However if we make denominator equal to zero: 2x+1 =0; x= -1/2

at x= -1/2 denominator =0 .F(x) becomes udnefined at this point.F(x) does not exist at such points

where denominator becomes zero.