Question

12. What are the values of A, B.C.respectively so that
x-1/x³+x=A/x +Bx+C/x²+1

Answer 1

The equation x-1/x³+x=A/x +Bx+C/x²+1 can be simplified by finding a common denominator.

Multiplying both sides of the equation by x³(x² + 1), we get:

x²(x² + 1) - x^2 = A(x² + 1) + Bx(x² + 1) + Cx³

Expanding the equation:

x^4 + x² - x² = Ax² + A + Bx³ + Bx + Cx³

Simplifying:

x^4 = (A + B)x³ + Ax² + Bx + A

Comparing the coefficients of the terms on both sides:

A + B = 0 (coefficient of x³)
A = 0 (coefficient of x²)
B = 0 (coefficient of x)
A = 0 (constant term)

From the first equation, we have A = -B.

Substituting this into the fourth equation, we get A = 0.

Therefore, the values of A, B, and C are 0, 0, and any real number respectively.