Answer:
The required domain is all real values of y, except y = 0 and [tex]y = \frac{b}{2}[/tex].
Step-by-step explanation:
The given expression is
[tex]\frac{b^{2} - 4by}{2y^{2} - by} - \frac{4y}{b - 2y}[/tex]
Let, [tex] x = \frac{b^{2} - 4by}{2y^{2} - by} - \frac{4y}{b - 2y}[/tex]
Therefore, to find the domain of this function means to find those values of variable y for which the x-value exists.
It is clear that the denominator of the two terms in the expression must not be zero for x to exist.
So, [tex]{2y^{2} - by} \neq 0[/tex]
⇒ [tex]y(2y - b) \neq 0[/tex]
⇒ [tex]y \neq 0 , y \neq \frac{b}{2}[/tex]
Again, [tex]b - 2y \neq 0[/tex]
⇒ [tex]y \neq \frac{b}{2}[/tex]
Therefore, the required domain is all real values of y, except y = 0 and [tex]y = \frac{b}{2}[/tex]. (Answer)
