If `(a^3+3ab^2)/(3a^2b+b^3) = 63/62` the find (5a-3b):(3a-b).

If (2a - 3b)/(2a+3b) = 1/3 , then find the value of (2a^(3) - 3b^(3))/(2a^(3) + 3b^(3)) .

a^(3)-b^(3)+1+3ab

If c be a whole number , but not a natural number and if (a^(2))/(b)+(b^(2))/(a)=3c " then find " (a^(3)+b^(3)+c^(3)-3abc).

(2a^(3)-b^(3))^(3)-b^(9)

If a = (sqrt5 + 1)/(sqrt5 + 1) and b = (sqrt5 -1)/(sqrt5 + 1) , then find the value of (a) (a^(2) + ab + b^(2))/(a^(2) - ab + b^(2)) (b) ((a -b)^(3))/((a + b)^(3)) (c) (3a^(2) + 5ab + b^(2))/(3a^(2) - 5ab + b^(2)) (d) (a^(3) + b^(3))/(a^(3) - b^(3))

If a = (sqrt3+1)/(sqrt3-1) and ab=1 , then find (a^(2) + ab + b^(2))

a+b+c=6,a^(2)+b^(2)+c^(2)=14 and a^(3)+b^(3)+c^(3)=36 then find the value of 3abc.

If a + b +5 = 0 , then find the value (a^(3)+b^(3)-15ab+125)

If a - b = - 1 then find the value of (a^(3)-b^(3)+3ab+1)

Prove that (a^(3/2)+ab)/(ab-b^3)-(sqrt(a))/(sqrt(a)-b)=(sqrt(a))/(b) .