I have to find $\alpha,\beta,\gamma,\delta \in \Bbb R $ such that
$$\lim \limits_{x \to 1} f(x) \in \Bbb R$$
where
$$f(x) = \begin{cases}\frac{\alpha x^3-(\beta+\gamma)x-(\alpha+\delta)}{(x-1)^2} & x < 1 \\ \frac{\beta x^2 - \alpha x + (\beta + \delta)}{x-1} & x > 1\end{cases}$$
I know that in order for the limit to exist, the side limits must be equal.
Trying to solve the first side limit, we find that the denominator is 0. To be able to use De L'Hospital Theorem the nominator must be 0.
So we get the equation: $\alpha - \beta-\gamma-\alpha-\delta = 0$
Doing the same for the other side limit we get: $\beta - \alpha + \beta+\delta = 0$
Is what i am doing correct?
If so, how do i continue to solve this?