Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$\frac { a \sqrt { x } - 3 } { a \sqrt { x } + 3 }$
A) $\frac { a ^ { 2 } x - 6 a \sqrt { x } - 9 } { a ^ { 2 } x + 9 }$
B) $\frac { a ^ { 2 } x + 6 a \sqrt { x } - 9 } { a ^ { 2 } x - 9 }$
C) $\frac { a ^ { 2 } x - 6 a \sqrt { x } + 9 } { a ^ { 2 } x - 9 }$
D) $\frac { a ^ { 2 } x - 6 a \sqrt { x } + 9 } { a ^ { 2 } x + 9 }$

Question

Quizplus · Accepted Answer

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

Rationalize the Denominator ax−3ax+3\frac { a \sqrt { x } - 3 } { a \sqrt { x } + 3 }ax​+3ax​−3​

Rationalize the Denominator $\frac { a \sqrt { x } - 3 } { a \sqrt { x } + 3 }$