Question

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

a. There is only one solution: x = 1. The solution x = 3 is an extraneous solution.
b. There are two solutions: x = 1 and x = 3.
c. There is only one solution: x = 3. The solution x = 1 is an extraneous solution.
d. There is only one solution: x = 1. The solution x = 0 is an extraneous solution.

Answer 1

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

Explanation:

Just took the test

Answer 2

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

Explanation:

We are given the following equation:

`\displaystyle(1)/(x) + (1)/(x-3) = (x-2)/(x-3)`

Solving the given equation, we have:

`\displaystyle(1)/(x) + (1)/(x-3) = (x-2)/(x-3)\\\\(2x-3)/(x(x-3))=(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.