Simplify by rationalizing the denominator.
-$\frac { \sqrt { x } - 3 } { \sqrt { x } + 3 }$
A) $- 6 \sqrt { x }$
B) $\frac { x - 6 \sqrt { x } + 9 } { x - 9 }$
C) $- 1$
D) $\frac { x + 9 } { x - 9 }$

Question

Quizplus · Accepted Answer

To rationalize the denominator of $\frac { \sqrt { x } - 3 } { \sqrt { x } + 3 }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $\sqrt { x } - 3$. This results in $\frac { (\sqrt { x } - 3)^2 } { (\sqrt { x } + 3)(\sqrt { x } - 3) }$. Simplifying, the numerator becomes $x - 6\sqrt { x } + 9$ and the denominator simplifies to $x - 9$, giving the expression $\frac { x - 6 \sqrt { x } + 9 } { x - 9 }$.

Simplify by Rationalizing the Denominator x−3x+3\frac { \sqrt { x } - 3 } { \sqrt { x } + 3 }x​+3x​−3​

Simplify by Rationalizing the Denominator $\frac { \sqrt { x } - 3 } { \sqrt { x } + 3 }$