Simplify by rationalizing the denominator.
-$\frac { y \sqrt { 2 } - 3 } { 2 \sqrt { 2 } + 3 }$
A) $\frac { y } { 2 } - 1$
B) $\frac { \mathrm { y } - 1 } { 3 }$
C) $\frac { 4 y - 3 y \sqrt { 3 } - 3 } { - 1 }$
D) $\frac { 4 y - 3 y \sqrt { 2 } - 6 \sqrt { 2 } + 9 } { - 1 }$

Question

Simplify by rationalizing the denominator.
-$\frac { y \sqrt { 2 } - 3 } { 2 \sqrt { 2 } + 3 }$
A) $\frac { y } { 2 } - 1$
B) $\frac { \mathrm { y } - 1 } { 3 }$
C) $\frac { 4 y - 3 y \sqrt { 3 } - 3 } { - 1 }$ 
D) $\frac { 4 y - 3 y \sqrt { 2 } - 6 \sqrt { 2 } + 9 } { - 1 }$

Quizplus · Accepted Answer

To rationalize the denominator of $\frac { y \sqrt { 2 } - 3 } { 2 \sqrt { 2 } + 3 }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $2\sqrt{2} - 3$. This eliminates the square root in the denominator and simplifies to the expression given in option D.

Simplify by Rationalizing the Denominator y2−322+3\frac { y \sqrt { 2 } - 3 } { 2 \sqrt { 2 } + 3 }22​+3y2​−3​

Simplify by Rationalizing the Denominator $\frac { y \sqrt { 2 } - 3 } { 2 \sqrt { 2 } + 3 }$