Solve y=(x^2+4)(x-1)/1-x

$$y= \frac{ ( { x }^{ 2 } +4)(x-1) }{ 1-x }$$

Solve for y

$$y=-\left(x^{2}+4\right)$$

$$x\neq 1$$

Solution Steps

Extract the negative sign in x-1.

$$y=\frac{-\left(-x+1\right)\left(x^{2}+4\right)}{-x+1}$$

Cancel out -x+1 in both numerator and denominator.

$$y=-\left(x^{2}+4\right)$$

To find the opposite of x^{2}+4, find the opposite of each term.

$$y=-x^{2}-4$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=i\sqrt{y+4}\text{, }&\text{unconditionally}\\x=-i\sqrt{y+4}\text{, }&y\neq -5\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=-\sqrt{-y-4}\text{, }&y\leq -4\\x=\sqrt{-y-4}\text{, }&y\neq -5\text{ and }y\leq -4\end{matrix}\right.$$