SOLUTION: If we rewrite the expression 4/x(x-1)(x-2) in the form (A/x)+ (B/x-1) + (C/x-2)
what are the values of A, B, and C?
Algebra.Com
Question 394712: If we rewrite the expression 4/x(x-1)(x-2) in the form (A/x)+ (B/x-1) + (C/x-2)
what are the values of A, B, and C?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
(x\ -\ 2)}\ =\ \frac{A}{x}\ +\ \frac{B}{x\ -\ 1}\ +\ \frac{C}{x\ -\ 2})
Apply the LCD in the RHS:
(x\ -\ 2)}\ =\ \frac{A(x\ -\ 1)(x\ -\ 2)\ +\ Bx(x\ -\ 2)\ +\ Cx(x\ -\ 1)}{x(x\ -\ 1)(x\ -\ 2)})
Expand the numerator in the RHS:
(x\ -\ 2)}\ =\ \frac{Ax^2\ -\ 3Ax\ +\ 2A\ +\ Bx^2\ -\ 2Bx\ +\ Cx^2\ -\ Cx)}{x(x\ -\ 1)(x\ -\ 2)})
Combine like terms in the RHS:
(x\ -\ 2)}\ =\ \frac{(A\ +\ B\ +\ C)x^2\ -\ (3A\ +\ 2B +\ C)x\ +\ 2A}{x(x\ -\ 1)(x\ -\ 2)})
Rewrite the numerator in the LHS:
(x\ -\ 2)}\ =\ \frac{(A\ +\ B\ +\ C)x^2\ -\ (3A\ +\ 2B +\ C)x\ +\ 2A}{x(x\ -\ 1)(x\ -\ 2)})
Equate the coefficients:
Solve the system for A, B, and C
John
My calculator said it, I believe it, that settles it
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