12. What are the values of A, B.C.respectively so that-

Question

x-1/x³+x=A/x +Bx+C/x²+1

Answer 1

To find the values of A, B, and C, we can equate the numerators on both sides of the equation and compare the coefficients of each power of x.

Starting with the left side of the equation:
x - 1/x³ + x

Expanding the denominator on the right side:
= A/(x) + Bx + C/(x² + 1)

Now, let's compare the coefficients of each power of x on both sides:
x term: 1 = Bx
Since the coefficient of x on the left side is 1 and there is no x term on the right side, B = 1.

x³ term: 0 = A/x³
Since there is no x³ term on the left side and the right side has a term with x in the denominator, A = 0.

x² term: 0 = C/(x² + 1)
Since there is no x² term on the left side and the right side has a term with x² in the denominator, C = 0.

Therefore, the values of A, B, and C are 0, 1, and 0 respectively.