Rationalize the denominator of the expression and simplify. $\frac { \sqrt { x } - 4 } { 2 \sqrt { x } - 7 }$
A) $\frac { 2 x + 15 \sqrt { x } - 4 } { 4 x - 7 }$
B) $\frac { 2 x - \sqrt { x } - 28 } { 4 x - 49 }$
C) $\frac { x - \sqrt { x } - 28 } { 2 x - 49 }$
D) $\frac { x + 15 \sqrt { x } - 4 } { 2 x - 7 }$
E) $\frac { 2 x + 9 \sqrt { x } - 4 } { 4 x - 7 }$

Question

Quizplus · Accepted Answer

To rationalize the denominator of $\frac { \sqrt { x } - 4 } { 2 \sqrt { x } - 7 }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $2\sqrt{x} + 7$. This process eliminates the square root from the denominator. After simplification, the correct answer is $\frac { 2 x - \sqrt { x } - 28 } { 4 x - 49 }$.

Rationalize the Denominator of the Expression and Simplify x−42x−7\frac { \sqrt { x } - 4 } { 2 \sqrt { x } - 7 }2x​−7x​−4​

Rationalize the Denominator of the Expression and Simplify $\frac { \sqrt { x } - 4 } { 2 \sqrt { x } - 7 }$