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The problem shown is written in Kazakh and asks for solving an equation. Let’s focus on the given equation:

### Given equation:
\[
\frac{3}{x} + \frac{4}{x - 1} = \frac{5 - x}{x^2 - x}
\]

#### Step 1: Simplify the right-hand side
Notice that the denominator \(x^2 - x\) can be factored:
\[
x^2 - x = x(x - 1)
\]
Thus, the equation becomes:
\[
\frac{3}{x} + \frac{4}{x - 1} = \frac{5 - x}{x(x - 1)}
\]

#### Step 2: Find a common denominator
The left-hand side has two fractions: \(\frac{3}{x}\) and \(\frac{4}{x - 1}\). Their common denominator is \(x(x - 1)\).

- Rewrite both fractions with this common denominator:
  \[
  \frac{3}{x} = \frac{3(x - 1)}{x(x - 1)}, \quad \frac{4}{x - 1} = \frac{4x}{x(x - 1)}
  \]

- Now, the left-hand side becomes:
  \[
  \frac{3(x - 1) + 4x}{x(x - 1)}
  \]

#### Step 3: Expand and combine terms in the numerator
\[
3(x - 1) + 4x = 3x - 3 + 4x = 7x - 3
\]
Thus, the equation becomes:
\[
\frac{7x - 3}{x(x - 1)} = \frac{5 - x}{x(x - 1)}
\]

#### Step 4: Eliminate the denominator by multiplying both sides by \(x(x - 1)\)
\[
7x - 3 = 5 - x
\]

#### Step 5: Solve the linear equation
Add \(x\) to both sides:
\[
7x + x - 3 = 5
\]
\[
8x - 3 = 5
\]
Add 3 to both sides:
\[
8x = 8
\]
Divide by 8:
\[
x = 1
\]

#### Step 6: Check for restrictions
The denominators \(x\) and \(x - 1\) must not be 0. Thus:
\[
x \neq 0 \quad \text{and} \quad x \neq 1
\]
Since \(x = 1\) is a solution, but it’s restricted, **there are no valid solutions**.

### Final Answer:
There are no solutions to the equation. 

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Would you like further clarification on any step?  

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Here are five related questions to practice:

1. How do you factor quadratic expressions like \(x^2 - x\)?
2. What are some techniques for solving equations with fractions?
3. How do you handle equations with no valid solutions due to restrictions?
4. What is the significance of finding a common denominator in equations?
5. How do you check for extraneous solutions when solving rational equations?

**Tip:** Always check for undefined values caused by the denominators before concluding a solution!

Solve the equation: 3/x + 4/(x - 1) = (5 - x)/(x^2 - x)

This solution covers the steps to solve the rational equation 3/x + 4/(x - 1) = (5 - x)/(x^2 - x). Learn key algebra concepts like factoring, finding common denominators, and handling restrictions on variable values. Suitable for Grades 9-11.

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