## Precalculus: Mathematics for Calculus, 7th Edition

$a)$ $x=4$ is a solution. $b)$ $x=8$ is not a solution.
$\dfrac{x^{3/2}}{x-6}=x-8$ $a)$ $x=4$ 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.