Answer
$a)$ $x=4$ is a solution.
$b)$ $x=8$ is not a solution.
Work Step by Step
$\dfrac{x^{3/2}}{x-6}=x-8$
$a)$ $x=4$
Substitute $x$ with $4$ and simplify both sides:
$\dfrac{(4)^{3/2}}{4-6}=4-8$
$\dfrac{\sqrt{4^{3}}}{-2}=-4$
$\dfrac{8}{-2}=-4$
$-4=-4$
Since the left side of the equation is equal to the right side, $x=4$ is a solution to this equation
$b)$ $x=8$
Substitute $x$ with $8$ and simplify both sides:
$\dfrac{(8)^{3/2}}{8-6}=8-8$
$\dfrac{\sqrt{8^{3}}}{2}=0$
$\dfrac{8\sqrt{8}}{2}=0$
$8\sqrt{2}\ne0$
Since the left side is not equal to the right side, $x=8$ is not a solution to this equation.
