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Answer:
Option A is correct.
i.e. x = 1, x = 0 is an extraneous solution.
Step-by-step explanation:
Given the expression
Solving the rational function
Apply fraction across multiply: if
Subtract x(4x+1) from both sides
Simplify
5x² - 4x² - x = 0
x² - x = 0
Factor x² - x = x(x-1)
so
x(x-1) = 0
Using the zero factor principle
if ab=0, then a=0 or b=0 (or both a=0 and b=0)
Thus, the solution to the equation is:
But, it is clear that if we substitute x = 0, the equation becomes undefined because we can not have the denominator to be 0.
In other words, the equation is undefined for x = 0
Thus, x = 0 is an extraneous solutions.
Therefore, option A is correct.
i.e. x = 1, x = 0 is an extraneous solution.