https://file.aiquickdraw.com/mathbot/file/1723641137303v976byv6.jpg

The new image clarifies the equation as:

\[
3x^{-\frac{1}{2}} - \frac{2\sqrt{x} + 4}{5x} = \frac{1}{\sqrt{2x}}
\]

This is the same equation as in the first image, so we can continue solving it with this correct format.

### Step-by-Step Solution:

1. **Rewrite the terms**:
   - \( 3x^{-\frac{1}{2}} \) can be written as \( \frac{3}{\sqrt{x}} \).
   - The term \( \frac{2\sqrt{x} + 4}{5x} \) remains as is.
   - The term \( \frac{1}{\sqrt{2x}} \) also remains as is.

   The equation is now:

   \[
   \frac{3}{\sqrt{x}} - \frac{2\sqrt{x} + 4}{5x} = \frac{1}{\sqrt{2x}}
   \]

2. **Multiply through by a common denominator**:

   Multiply every term by \( 5\sqrt{2x} \) to eliminate the square roots and fractions:

   - \( \frac{3}{\sqrt{x}} \cdot 5\sqrt{2x

Learn how to solve the equation 3x^(-1/2) - (2√(x) + 4)/(5x) = 1/√(2x) step-by-step. This problem involves equations with exponents and fractional expressions, covering key algebraic concepts and manipulation techniques. Suitable for students in Grades 10-12.

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