Question

divide by factor method : x⁴ -1/x²-1​

Answer 1

$\frac{x^{4} - 1 }{x^{2} - 1 }$

$= \frac{(x^{2})^{2} - 1^{2} }{x^{2} - 1 }$

/* By algebraic identity */

$\boxed{ \pink{ a^{2} - b^{2} = ( a + b )( a - b ) }}$

$= \frac{ (x^{2} + 1)\cancel {(x^{2} - 1)} }{\cancel { (x^{2} - 1) }}$

$= x^{2} + 1$

Therefore.,

$\red{ \frac{x^{4} - 1 }{x^{2} - 1 } }\green { = x^{2} + 1 }$

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Answer 2

Given Equation :-

$\sf\blue{ \dfrac{ {x}^{4} - 1 }{ {x}^{2} - 1} }$

Solution :-

Take Out Common Factors.

$\implies\sf {\dfrac{ { {(x}^{2} )}^{2} - 1}{ {x}^{2} - 1 } }$

Now, Use Identity :- a² - b² = (a + b)(a - b).

$\implies\sf{ \dfrac{( {x}^{2} + 1)(\cancel{{x}^{2} - 1) }}{\cancel{ {x}^{2} - 1 } }}$

$\sf\implies\red{ {x}^{2} + 1}$

Therefore, The Required Answer :-

$\sf{ \dfrac{ {x}^{4} - 1 }{ {x}^{2} - 1} } =$ $\sf\green{ {x}^{2} + 1}$