For `x=(1)/(2)` and `y=(2)/(3)`, verify that `-(x+y) =(-x)+(-y)`.

(x) / (2) + (y) / (3) = 1 (x) / (3) + (y) / (2) = 1

If x and y are of same sign,then the value of (x^(3))/(2)cos ec^(2)((1)/(2)(tan^(-1)x)/(y))+(y^(3))/(2)sec^(2)((1)/(2)(tan^(-1)y)/(x)) is equal to (x-y)(x^(2)+y^(2)) (b) (x+y)(x^(2)-y^(2))(x+y)(x^(2)+y^(2))*(d)(x-y)(x^(2)-y^(2))

If the points (x_(1),y_(1)),(x_(2),y_(2)), and (x_(3),y_(3)) are collinear show that (y_(2)-y_(3))/(x_(2)x_(3))+(y_(3)-y_(1))/(x_(3)x_(1))+(y_(1)-y_(2))/(x_(1)x_(2))=0

Simplify : (i) (5x - 9y) - (-7x + y) (ii) (x^(2) -x) -(1)/(2)(x - 3 + 3x^(2)) (iii) [7 - 2x + 5y - (x -y)]-(5x + 3y -7) (iv) ((1)/(3)y^(2) - (4)/(7)y + 5) - ((2)/(7)y - (2)/(3)y^(2) + 2) - ((1)/(7)y - 3 + 2y^(2))

Verify the property x xx y = y xx x of rational numbers by using x=(2)/(3) and y=(9)/(4) and What is the name of this property?

(x + 2) (x + 1) = (x -2) (x -3) (y+3)(y+2)=(y-1)(y-2)

If ((2x-y)/(x+2y))=(1)/(2), then find the value of ((3x-y)/(3x+y))

If the tangent at (x_(1),y_(1)) to the curve x^(3)+y^(3)=a^(3) meets the curve again in (x_(2),y_(2)), then prove that (x_(2))/(x_(1))+(y2)/(y_(1))=-1