https://file.aiquickdraw.com/mathbot/file/1726575964354efugmtn0.jpg

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:

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


Simplify the expression: (3 / (2√2 - 4)) - ((3 - √2) / (√2 + 1))

Learn how to simplify the expression (3 / (2√2 - 4)) - ((3 - √2) / (√2 + 1)) using rationalization techniques. This problem covers key algebraic concepts, including rationalizing denominators and applying the difference of squares formula. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation