Question

Given that `d/dx ((1+x^2+x^4)/(1+x+x^2))=Ax+B` What is the value of `A?`
A. `-1`
B. 1
C. 2
D. 4

Answer 1

Correct Answer - C
Given `(d)/(dx)((1+x^(2)+x^(4))/(1+x+x^(2)))`
`=(d)/(dx)[(1+x+x^(2)+x^(4)-x)/(1+x+x^(2))]`
`=(d)/(dx)[1+(x^(4)-x)/(x^(2)+x+1)]`
`=(d)/(dx)[1+(x(x^(3)-1))/(x^(2)+x+1)]`
`=(d)/(dx)[1+x(x-1)]`
`=(d)/(dx)[1+x^(2)-x]-2x - 1" "...(i)`
Now comparing equation (i) with AX + B, we get A = 2 and B = -1.