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Let's analyze the given equation.
$x−34 =x−3x $
We are asked to check if either $3$ or $4$ are extraneous solutions. An extraneous solution is a solution that emerges from the process of solving the problem, but is not a valid solution of the equation. First, let's check if $x=4$ is a solution by substituting it into the equation.
Since the substitution of $x=4$ produces a true statement, the solution $x=4$ is a valid one. Next, Let's check $x=3.$
Notice that in this case we get that the denominator is $0,$ which is impossible. Therefore, $x=3$ is not a valid solution, so it is an extraneous solution.

$x−34 =x−3x $

Substitute$x=4$

$4−34 =?4−34 $

SubTermsSubtract terms

$14 =?14 $

CalcQuotCalculate quotient

$4=4✓$