Изображение упражнения

Amanita, let's carefully analyze the content inside the green rectangle and the rest of the image to understand what needs to be solved.

Step-by-step Plan:

  1. Identify the Expressions: The green rectangle contains the quadratic expression 3x210x+83x^2 - 10x + 8. Below it, there is another expression: 24x224x^2.
  2. Determine the Relationship: Since both expressions are shown, we might be asked to compare, simplify, or relate them. A common task is to divide the quadratic by the monomial, i.e., 3x210x+824x2\frac{3x^2 - 10x + 8}{24x^2}.
  3. Simplify the Expression: To simplify, we will divide each term in the numerator by the denominator.
  4. Present the Simplified Form: Write the final answer in the simplest form.

Let's execute these steps:

Step 1: Write the Division Expression

We set up the division as:

3x210x+824x2\frac{3x^2 - 10x + 8}{24x^2}

Step 2: Divide Each Term

We divide each term in the numerator by 24x224x^2:

3x224x210x24x2+824x2\frac{3x^2}{24x^2} - \frac{10x}{24x^2} + \frac{8}{24x^2}

Step 3: Simplify Each Fraction

Let's simplify each term:

  • 3x224x2\frac{3x^2}{24x^2}
  • 10x24x2\frac{10x}{24x^2}
  • 824x2\frac{8}{24x^2}

I will now simplify each term.

Simplifying 3x224x2\frac{3x^2}{24x^2}:

3x224x2=324=18\frac{3x^2}{24x^2} = \frac{3}{24} = \frac{1}{8}

Simplifying 10x24x2\frac{10x}{24x^2}:

10x24x2=10241x=512x\frac{10x}{24x^2} = \frac{10}{24} \cdot \frac{1}{x} = \frac{5}{12x}

Simplifying 824x2\frac{8}{24x^2}:

824x2=13x2\frac{8}{24x^2} = \frac{1}{3x^2}

Step 4: Combine the Results

So, the simplified form is:

18512x+13x2\frac{1}{8} - \frac{5}{12x} + \frac{1}{3x^2}


Final Answer:

Amanita, the simplified form of 3x210x+824x2\frac{3x^2 - 10x + 8}{24x^2} is:

18512x+13x2\boxed{\frac{1}{8} - \frac{5}{12x} + \frac{1}{3x^2}}