5/7x + 1/3x -0,75 • 2/3x

To simplify the expression \( \frac{5}{7}x + \frac{1}{3}x - 0.75 \cdot \frac{2}{3}x \), we will follow these steps:

1. First, let's convert \( 0.75 \) to a fraction. Since \( 0.75 = \frac{3}{4} \), we can rewrite the expression:

   \[ \frac{5}{7}x + \frac{1}{3}x - \frac{3}{4} \cdot \frac{2}{3}x \]

2. Now, calculate \( \frac{3}{4} \cdot \frac{2}{3} \):

   \[ \frac{3}{4} \cdot \frac{2}{3} = \frac{3 \cdot 2}{4 \cdot 3} = \frac{6}{12} = \frac{1}{2} \]

   Thus, the expression becomes:

   \[ \frac{5}{7}x + \frac{1}{3}x - \frac{1}{2}x \]

3. To combine these fractions, we need a common denominator. The least common multiple of \(7\), \(3\), and \(2\) is \(42\).

4. Convert each term to have a denominator of \(42\):

   • For \( \frac{5}{7}x \): \[ \frac{5}{7}x = \frac{5 \cdot 6}{7 \cdot 6}x = \frac{30}{42}x \]

   • For \( \frac{1}{3}x \): \[ \frac{1}{3}x = \frac{1 \cdot 14}{3 \cdot 14}x = \frac{14}{42}x \]

   • For \( \frac{1}{2}x \): \[ \frac{1}{2}x = \frac{1 \cdot 21}{2 \cdot 21}x = \frac{21}{42}x \]

5. Now, substitute these back into the expression:

   \[ \frac{30}{42}x + \frac{14}{42}x - \frac{21}{42}x \]

6. Combine the fractions:

   \[ \left( \frac{30 + 14 - 21}{42} \right)x = \frac{23}{42}x \]

Thus, the simplified expression is:

\[ \frac{23}{42}x \]