$$ \frac { \sqrt[ 3 ] { x ^ { 2 } } + 2 \sqrt[ 3 ] { x } + 1 } { x + 3 \sqrt[ 3 ] { x ^ { 2 } } + 3 \sqrt[ 3 ] { x } + 1 } - \frac { 1 } { \sqrt[ 3 ] { x } + 1 } $$

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UpStudy AI · Accepted Answer

Berilgan ifodani quyidagicha soddalashtirish mumkin:

$$
\frac{ \sqrt[3]{x^2} + 2 \sqrt[3]{x} + 1 }{ x + 3 \sqrt[3]{x^2} + 3 \sqrt[3]{x} + 1 } - \frac{1}{ \sqrt[3]{x} + 1 }
$$

**Qadamlar:**

1. **O'zgartirish:** 
   $$\sqrt[3]{x} = y$$ deb olamiz. Shunda:
   $$
   \sqrt[3]{x^2} = y^2 \quad \text{va} \quad x = y^3
   $$

2. **Ifodani almashtirish:**
   $$
   \frac{y^2 + 2y + 1}{y^3 + 3y^2 + 3y + 1} - \frac{1}{y + 1}
   $$

3. **Polinomlarni faktorizatsiya qilish:**
   - $$y^2 + 2y + 1 = (y + 1)^2$$
   - $$y^3 + 3y^2 + 3y + 1 = (y + 1)^3$$

4. **Ifodani soddalashtirish:**
   $$
   \frac{(y + 1)^2}{(y + 1)^3} - \frac{1}{y + 1} = \frac{1}{y + 1} - \frac{1}{y + 1} = 0
   $$

**Natija:**
Berilgan ifoda nolga teng.
Berilgan ifoda nolga teng.

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