In general as we know fraction is define for all number only there is one condition that denominator can not be equal to zero.
So let's find first where denominator is equal to zero.
For that we can solve
[tex]4x^2 - 21x - 18 = 0[/tex]
Now we can solve it by factoring.
As we know -18 * 4 = -72
So we have to break -72 in such two parts whose summation equal to -21x and multiplication equal to -72.
So we can write -72 as = -24 * 3
Because when we add -24 and 3 we will get -21
So we can write equation as
[tex]4x^2 -24x + 3x - 18 = 0[/tex]
[tex]4x(x-6) +3(x-6) = 0[/tex]
[tex](x-6)(4x+3) = 0[/tex]
SO we can say x = 6 or x = [tex] \frac{-3}{4} [/tex]
So we can say our fraction is define for all real number but x can not be equal to 6 or [tex] \frac{-3}{4} [/tex] because at these values denominator is zero.
SO domain is set of all real number expect x = 6 or [tex]x = \frac{-3}{4} [/tex]
