y^(2)-sqrt(x^(2)-2x+10)

Simplify : (sqrt(x^(2)+y^(2))-y)/(x-sqrt(x^(2)-y^(2))) div (sqrt(x^(2)-y^(2))+x)/(sqrt(x^(2)+y^(2))+y)

Simplify : (sqrt(x^(2)+y^(2))-y)/(x-sqrt(x^(2)-y^(2)))-:(sqrt(x^(2)-y^(2))+x)/(sqrt(x^(2)+y^(2))+y)

Simplify : (a) sqrt(y+sqrt(2xy-x^(2))) + sqrt(y-sqrt(2xy-x^(2))) (b) (x+sqrt(x^2-1))/(x-sqrt(x^(2)-1)) -(x-sqrt(x^(2)-1))/(x+sqrt(x^(2)-1))

Show that: (x^((2)/(3))sqrt(y^(-2)))/(y^(2)sqrt(x^(-2)))times(y^(2)sqrt(x^(-2)))/(sqrt(x^((4)/(3))))=(1)/(y)

A: The distance of the (1,2,3) from the coordinate axes are sqrt(13) , sqrt(10),sqrt(5) R : The distance of P (x,y,z) from the coordinate are sqrt(y^(2)+z^(2)),sqrt(x^(2)+z^(2)),sqrt(x^(2)+y^(2))

Rationalise the denominator: (a) (1)/(root(3)(3) + root(3)(2)) , (b) (2)/(sqrt5 + sqrt3 + sqrt2) , (c) (x^(2))/(sqrt(x^(2) + y^(2)) - y) , (d) (1)/(sqrt6 + sqrt5 - sqrt11) (e) (sqrt(x + 2y) - sqrt(x -2y))/(sqrt(x + 2y) + sqrt(x - 2y)) , (f) (sqrt10 + sqrt5 - sqrt3)/(sqrt10 - sqrt5 + sqrt3)

Simplify : (sqrt(x^(2)+y^(2))-y)/(x-sqrt(x^(2)+y^(2)))-:(sqrt(x^(2)+y^(2))+x)/(sqrt(x^(2)+y^(2))+y)

Evaluate (sqrt(x^2-y^2)+x)/(sqrt(x^2+y^2)+y) divide (sqrt(x^2+y^2)-y)/(x-sqrt(x^2-y^2))

If sqrt(a+ib)=x+iy, then possible value of sqrt(a-ib) is x^(2)+y^(2) b.sqrt(x^(2)+y^(2)) c.x+iydx-iy e.sqrt(x^(2)-y^(2))

If xy=a[y+sqrt(y^(2)-x^(2))] , prove that, x^(3)(dy)/(dx)=y^(2)(y+sqrt(y^(2)-x^(2)))