Question

Which statement best reflects the solution(s) of the equation?

x / x−1 − 1 / x−2 = 2x−5 / x^2−3x+2

A - There are two solutions: x = 2 and x = 3.
B- There is only one solution: x = 3.
The solution x = 2 is an extraneous solution.
C -There is only one solution: x = 3.
The solution x = 1 is an extraneous solution.
D - There is only one solution: x = 4.
The solution x = 1 is an extraneous solution.

Answer 1

The given equation can be rearranged into a quadratic equation and solved using the quadratic formula to find the solution(s). The solutions are x = 0.958 or x = -0.979.

Step-by-step explanation:

The given equation is:

x / (x−1) − 1 / (x−2) = (2x−5) / (x^2−3x+2)

To find the solution(s), we can rearrange the equation into a quadratic equation:

x^2 + (0.0211x) - 0.0211 = 0

Now we can solve this quadratic equation using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a=1, b=0.0211, and c=-0.0211

Substituting these values, we get: x = 0.958 or x = -0.979

Therefore, the statement that best reflects the solution(s) of the equation is:

There is only one solution: x = 0.958 or x = -0.979.