from PIL import Image import pytesseract

Load the uploaded image

image_path = "/mnt/data/1731998136182gt955fqg.jpg" image = Image.open(image_path)

Use pytesseract to extract the mathematical content from the image

extracted_text = pytesseract.image_to_string(image, config='--psm 6') extracted_text"4x‘ - (Gy) '\nge 5 ‘a\n""4x‘ - (Gy) '\nge 5 ‘a\n"successThe extracted mathematical expression is unclear, but it seems to resemble:

$\frac{4x^{-1} - (5y)^{-1}}{x^{-2}} = \, ?$

I will interpret and solve it accordingly. Let's simplify the given expression step by step:

Expression:

$\frac{4x^{-1} - (5y)^{-1}}{x^{-2}}$

Step-by-step simplification:

1. Rewrite the terms with positive exponents:

   • $4x^{-1} = \frac{4}{x}$
   • $(5y)^{-1} = \frac{1}{5y}$
   • $x^{-2} = \frac{1}{x^2}$

   Substituting these into the expression gives: $\frac{\frac{4}{x} - \frac{1}{5y}}{\frac{1}{x^2}}$

2. Multiply the numerator by the reciprocal of the denominator: $\left(\frac{4}{x} - \frac{1}{5y}\right) \times x^2$

3. Expand and simplify: $\frac{4}{x} \cdot x^2 = 4x$ $\frac{1}{5y} \cdot x^2 = \frac{x^2}{5y}$

   So the expression becomes: $4x - \frac{x^2}{5y}$

4. Combine into a single fraction: $\frac{20xy - x^2}{5y}$

Final Answer:

$\frac{20xy - x^2}{5y}$

Would you like further explanation or a deeper breakdown of any steps?

Related Questions:

1. How do negative exponents work in general?
2. Can this expression be simplified further for specific values of $x$ and $y$?
3. What happens if $y = 0$ in this expression?
4. How would this change if the powers in the numerator were positive?
5. Can you derive the same result using a different algebraic method?

Tip:

When simplifying algebraic fractions, always aim to rewrite negative exponents as positive for better clarity.