Question

(x^4-1)=(x^2-1)*a,then a=

Answer 1

Answer:

$a = x^{2}+1$

Step-by-step explanation:

$x^{4}-1=(x^{2}-1)a$

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

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

$\implies x^{2}+1 = a$

Therefore,

$a = x^{2}+1$

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Answer 2

Answer:

$a = (x^{2}+1)$

Step-by-step explanation:

The given equation is-

$(x^{4} - 1) = (x^{2}  -1)a$     ----------- 1

a =?

From equation 1

$(x^{4} - 1) = (x^{2}  -1)a$

$[(x^{2} )^{2} -1] = (x^{2} -1)a$

We know that-

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

$(x^{2} + 1)(x^{2} - 1) = (x^{2} - 1)a$

Hence, $a = (x^{2}+1)$