The equation shown in the image appears to be a limit problem. Here's the expression I can read from the image:

$\lim_{{x \to 7}} \frac{(2x - 3)^2 - (x + 1)^2}{x - 7}$

This looks like a classic limit problem where direct substitution may lead to an indeterminate form (like $\frac{0}{0}$), so we would need to simplify the expression using algebraic techniques, such as factoring or applying difference of squares.

Let's solve this step by step:

1. The numerator is of the form $(2x - 3)^2 - (x + 1)^2$, which is a difference of squares. We can apply the identity:

[ a^2 - b^2 = (a