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Question
The value of `(1 - x^4)/(1 + x) ÷ (1 + x^2)/x xx 1/(x(x - 1))` is: (If x is not equal to, 0, – 1, 1)
Options
2
0
1
– 1
MCQ
Solution
– 1
Explanation:
`(1 - x^4)/(1 + x) ÷ (1 + x^2)/x xx 1/(x(x - 1))`
`((1)^2 - (x^2)^2)/(1 + x) ÷ (1 + x^2)/x xx 1/(x(x - 1))`
= `((1 - x^2)(1 + x^2))/(1 + x) xx x/((1 + x^2)) xx 1/(x(x - 1))`
= `(1 - x^2)/((1 + x)(x - 1)) = (1^2 - x^2)/((1 + x)(x - 1))`
= `((1 + x)(1 - x))/((1 + x)(x - 1)) = ((1 - x))/((x - 1))`
Let `x` = 2
`((1 - 2))/((2 - 1)) = (-1)/1` = – 1
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Algebraic Identities and Polynomials (Entrance Exam)
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