Solve for x if x squared minus one over x minus one is equal to 4

The equation "x squared minus one over x minus one is equal to 4" can be written as:

$$\frac{x^2 - 1}{x - 1} = 4$$

The numerator $x^2 - 1$ is a difference of squares, which can be factored as $(x-1)(x+1)$.

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

We can cancel out the $(x-1)$ term from the numerator and the denominator, provided that $x-1 \neq 0$, which means $x \neq 1$.

$$x + 1 = 4$$

Subtract 1 from both sides of the equation:

$$x = 4 - 1$$ $$x = 3$$

Since our solution $x=3$ is not equal to 1, it is a valid solution.

The value of $x$ is $\boxed{3}$.