If `y=(ax^2)/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+c/(x-c)+1` then `(y prime)/y=`

If y=(ax^(2))/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+(c)/(x-c)+1 then (y')/(y)=

If y=(ax^(2))/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+(c)/(x-c)+1 find (dy)/(dx)

If y=(ax^(2))/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+(c)/(x-c)+1 then prove that (y')/(y)=(1)/(x)[(a)/(a-x)+(b)/(b-x)+(c)/(c-x)]

Prove that (ax^(2))/((x -a)(x-b)(x-c))+(bx)/((x -b)(x-c))+(c)/(x-c)+1 = (x^(3))/((x-a)(x-b)(x-c)) .

int(ax^(2)+bx+c)/((x-a)(x-b)(x-c))dx;a,b,c are distinct

If f((ax+b)/(x-a))=x, then f^(-1)(x)= (a) x (b) (bx+a)/(x-b)( c) f(x)

Let P(x)=((x-a)(x-b))/((c-a)(c-b))c^(2)+((x-b)(x-c))/((a-b)(a-c))a^(2)+((x-c)(x-a))/((b-c)(b-a))b^(2) Prove that P(x) has the property that P(y)=y^(2) for all y in R .

If (x^(4)+1)/((x-1)(x-2))=Ax^(2)+Bx+C-(2)/(x-1)+(17)/(x-2) then, the values of A, B and C are ?

Statement-1: If a, b, c are distinct real numbers, then a((x-b)(x-c))/((a-b)(a-c))+b((x-c)(x-a))/((b-c)(b-a))+c((x-a)(x-b))/((c-a)(c-b))=x for each real x. Statement-2: If a, b, c in R such that ax^(2) + bx + c = 0 for three distinct real values of x, then a = b = c = 0 i.e. ax^(2) + bx + c = 0 for all x in R .

If (a)/(x-a) + (b)/(y-b) + (c )/(z-c)=2 find (x)/(x-a) + (y)/(y-b) + (z)/(z-c) = ?