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

If f(x)= |1 x x+1 2x x(x-1)(x+1)x3x(x-1)x(x-1)(x-2)(x+1)x(x-1)| then f(500) is equal to a. 0 b. 1 c. 500 d. -500

If f(x)= |1 x x+1 2x x(x-1)(x+1)x3x(x-1)x(x-1)(x-2)(x+1)x(x-1)| then f(500) is equal to a. 0 b. 1 c. 500 d. -500

What is (8x)/(1-x^(4)) - (4x)/(x^(2) +1) +(x+1)/(x-1) - (x-1)/(x+1) equal to?

Solve by factorization: (x+1)/(x-1)-(x-1)/(x+1)=5/6,\ \ x!=1,\ -1

Solve by factorization: (x+1)/(x-1)-(x-1)/(x+1)=(5)/(6),x!=1,-1

If f(x)=|{:(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-1)):}| then

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),x(x-1)(x-2),x(x+1)(x-1))| , using properties of determinant, find f(2x) - f(x).