Asked by YikOn Cheung on May 06, 2024
Verified
Rationalize the denominator of the expression and simplify. x−42x−7\frac { \sqrt { x } - 4 } { 2 \sqrt { x } - 7 }2x−7x−4
A) 2x+15x−44x−7\frac { 2 x + 15 \sqrt { x } - 4 } { 4 x - 7 }4x−72x+15x−4
B) 2x−x−284x−49\frac { 2 x - \sqrt { x } - 28 } { 4 x - 49 }4x−492x−x−28
C) x−x−282x−49\frac { x - \sqrt { x } - 28 } { 2 x - 49 }2x−49x−x−28
D) x+15x−42x−7\frac { x + 15 \sqrt { x } - 4 } { 2 x - 7 }2x−7x+15x−4
E) 2x+9x−44x−7\frac { 2 x + 9 \sqrt { x } - 4 } { 4 x - 7 }4x−72x+9x−4
Rationalize
The process of eliminating radicals from the denominator of a fraction or complex numbers from the denominator.
Denominator
The lower segment of a fraction representing the number of parts into which the total is split.
- Acquire the ability to rationalize the denominator in fractions that include square roots.
Verified Answer
ZK
Zybrea KnightMay 07, 2024
Final Answer :
B
Explanation :
To rationalize the denominator of x−42x−7\frac { \sqrt { x } - 4 } { 2 \sqrt { x } - 7 }2x−7x−4 , multiply both the numerator and the denominator by the conjugate of the denominator, which is 2x+72\sqrt{x} + 72x+7 . This process eliminates the square root from the denominator. After simplification, the correct answer is 2x−x−284x−49\frac { 2 x - \sqrt { x } - 28 } { 4 x - 49 }4x−492x−x−28 .
Learning Objectives
- Acquire the ability to rationalize the denominator in fractions that include square roots.