The expression shown in the image is:

$\frac{3}{2\sqrt{2} - 4} - \frac{3 - \sqrt{2}}{\sqrt{2} + 1}$

To simplify this expression, we will work with each fraction separately and then combine them.

Step 1: Rationalize the denominators

Rationalize the denominators of both fractions.

First Fraction: $\frac{3}{2\sqrt{2} - 4}$

We rationalize the denominator by multiplying both the numerator and the denominator by the conjugate $2\sqrt{2} + 4$:

$\frac{3}{2\sqrt{2} - 4} \times \frac{2\sqrt{2} + 4}{2\sqrt{2} + 4} = \frac{3(2\sqrt{2} + 4)}{(2\sqrt{2})^2 - 4^2}$

Simplifying the denominator:

$(2\sqrt{2})^2 = 8, \quad 4^2 = 16$ [