- x
^{2}+ 1 - x
^{2}- x + 1 - x
^{2}- 1 - x
^{2}+ x + 1

Option 2 : x^{2} - x + 1

**Given**

**\(\frac {(x^4 + x^2 + 1)} {(x^2 + x+ 1)}\)**

**Formula used**

(a + b)^{2} = a^{2} + b^{2} + 2ab

a^{2} - b^{2} = (a + b)(a - b)

**Calculation:**

\(\frac {(x^4 + x^2 + 1)} {(x^2 + x+ 1)}\)

⇒ [(x^{4} + 2x^{2} + 1) - x^{2}]/(x^{2} + x + 1)

⇒ [(x^{2} + 1)^{2} - x^{2}]/(x^{2} + x + 1)

Apply this formula a2 - b2 = (a + b)(a - b)

⇒ [(x^{2} + 1 + x)(x^{2} + 1 - x)]/(x2 + x + 1)

⇒ x^{2} - x + 1

**∴ The required answer is x2 - x + 1**

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