`x/(x - y) - y/(x + y)=..`

Simplify the following : (x - y)(y - x) + (x + y)(x - 2y)

The sum of the GP (x+y)/(x-y), 1, (x-y)/(x+y),.....

Solve the following system of equations: (x+y)/(x y)=2,\ \ \ (x-y)/(x y)=6

The third proportional to (x^(2)-y^(2)) and (x-y) is (x+y) b.(x-y)c(x+y)/(x-y) d.(x-y)/(x+y)

When simplified (x^(-1)+y^(-1))^(-1) is equal to (a)\ x y (b) x+y (c) (x y)/(x+y) (d) (x+y)/(x y)

Find the sum of G.P. : (x+y)/(x-y)+1+(x-y)/(x+y)+ . . . . .. . . . upto n terms.

The following steps are involved in the factorisation of x^(2) (x - y) + (y-x) y^(2) . Arrange them in sequential order from the first to the last . (A) (x-y) [x^(2) - y^(2)] (B) x^(2)(x-y) - ( x- y) y^(2) (C) (x-y)^(2) (x + y) (D) (x-y) [(x + y)( x-y)]