Finding the value of a variable present in two functions

Question

I have two functions each containing a variable besides an $x$.

$$kx-3\quad \text{ and }\quad x^2+k$$

I set them equal to each other, but my algebra is failing me and I can't remember how to solve for $k$

$$kx-3=x^2+k$$

Answer 1

Bring the terms involving $k$ together on one side, factor the $k$ out, then divide through: \begin{align*} kx - 3 &= x^2 + k \\ kx - k &= x^2 + 3 \\ k(x - 1) &= x^2 + 3 \\ k &= \frac{x^2 + 3}{x - 1} \end{align*}