Perform the operation and simplify such that: 1/x+3 + 3/x-3 = ax+b/x²-c

Question

a=
b=
c=

Answer 1

To simplify the equation, we need to find a common denominator for the fractions on the left side of the equation.

1/x + 3/x = (1+3)x/(x(x-3)) = 4x/(x(x-3))

So the left side of the equation becomes:

4x/(x(x-3)) = ax + b/x² - c

Now we can try to find the values of a, b, and c by comparing the numerators on both sides of the equation.

4x = ax(x-3) + b

Expanding the right side, we get:
4x = ax² - 3ax + b

Now we need to find a, b by comparing coefficients:

a = 4 (coefficient of x² term)

-3a = 0 (coefficient of x term on both sides of the equation)

b = 0 (constant term)

Therefore, a = 4, b = 0, and c = 3 (coefficient of x term in the denominator).

So the simplified equation is: 4x/(x(x-3)) = 4x/x².