Question

Which statement best reflects the solution(s) of the equation? 1/x+1/x−3=x−2/x−3

Answer 1

Answer:

Option A) There is only one solution: x = 1. The solution x = 3 is an extraneous solution.                

Step-by-step explanation:

We are given the following equation:

$\displaystyle\frac{1}{x} + \frac{1}{x-3} = \frac{x-2}{x-3}$

Solving the given equation, we have:

$\displaystyle\frac{1}{x} + \frac{1}{x-3} = \frac{x-2}{x-3}\\\\\frac{2x-3}{x(x-3)}=\frac{x-2}{x-2}\\\\2x-3 = x^2 - 2x\\x^2 - 4x + 3 = 0\\x^2 - x-3x + 3 = 0\\x(x-1)-3(x-3) = 0\\(x-3)(x-1) = 0\\x =1, x=3$

Extraneous solutions:

• An extraneous solution is not a root of the original equation because it was excluded from the domain of the original equation.

• We may arrive to this solution but cannot consider it as a solution because it is not valid.

But x = 3 cannot be a solution to the given equation as when put in the given equation it gives denominator zero.

Thus, x = 1 is the solution of the given equation and x = 3 is an extraneous solution.

Answer 2

It is a i hope that help