`(x-1)/x + (x+1)/x < 2`

Using the properties of determinants, prove that following : |{:(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(1-x),x(x-1)(x-2),x(x+1)(x-1)):}|=6x^(2)(1-x^(2))

prove that |(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(1-x),x(x-1)(x-2),x(x+1)(x-1))|=6x^(2)(1-x^(2))

If f(x) =|(1, x, x+1),(2x, x(x-1), x(x+1)), (3x(x-1), 2(x-1)(x-2), x(x+1)(x-1))| then what is f(-1) +f(0) +f(1) equal to ?

Let f(x)=x((1)/(x-1)+(1)/(x)+(1)/(x+1)),x>1

Let f(x)=x((1)/(x-1)+(1)/(x)+(1)/(x+1)), x gt 1 . Then

Let f(x) = x(1/(x - 1) + 1/x + 1/(x + 1)), x gt 1 , Then

If y=x+(1)/(x+(1)/(x+(1)/(x+(1)/(x+...)))), prove that (dy)/(dx)=(1)/(2(x)/(x+(1)/(x+(1)/(x+1))))