" 93."(x^(-3)-y^(-3))/(x^(-3)y^(-1)+(xy)^(2)+y^(-3)x^(-1))

Verify : (i) x^(3)+y^(3)=(x+y)(x^(2)-xy+y^(2)) (ii) x^(3)-y^(3)=(x-y)(x^(2)+xy+y^(2))

Veriffy : (i) x^(3)+y^(3)=(x+y)(x^(2)-xy+y^(2))x^(3)-y^(3)=(x-y)(x^(2)+xy+y^(2))

Verify : (i) x^(3)+y^(3)=(x+y)(x^(2)-xy+y^(2)) " " (ii) x^(3)-y^(3)=(x-y)(x^(2)+xy+y^(2))

Add : x^(3) - x^(2)y + 5xy^(2) + y^(3) , -x^(3) - 9xy^(2) + y^(3), 3x^(2)y + 9xy^(2)

If S_(n)=(x+y)+(x^(2)+xy+y^(2))+(x^(3)+x^(2)y+y^(2)x+y^(3))+…n terms then prove that (x-y)S_(n)=[(x^(2)(x^(n)-1))/(x-1)-(y^(2)y^(n)-1)/(y-1)] .

Solve the differential equation _(y-3)(dy)/(dx)=((x+1)^(2)+(y-3)^(2)e^((y-3)/(x-1)))/((xy-3x+y-3)e^(x+1))

If |x|<1 and |y|<1, find the sum of infinity of the following series: (x+y)+(x^(2)+xy+y^(2))+(x^(3)+x^(2)y+xy^(2)+y^(3))+

The factors of x^(3)-1+y^(3)+3xy are (a) (x-1+y)(x^(2)+1+y^(2)+x+y-xy)( b) (x+y+1)(x^(2)+y^(2)+1-xy-x-y)( c) (x-1+y)(x^(2)-1-y^(2)+x+y+xy)(d)3(x+y-1)(x^(2)+y^(2)-1)

If x+y+z=xyz , prove that: a) (3x-x^(3))/(1-3x^(2))+(3y-y^(3))/(1-3y^(2))+(3z-z^(3))/(1-3z^(2))= (3x-x^(3))/(1-3x^(2)).(3y-y^(3))/(1-3y^(2)).(3z-z^(3))/(1-3z^(2)) b) (x+y)/(1-xy) + (y+z)/(1-yz)+(z+x)/(1-zx)= (x+y)/(1-xy) .(y+z)/(1-yz).(z+x)/(1-zx)