Simplify the expression. Do not rationalize the denominator.
-$$2 x \sqrt { 3 x - 4 } + x ^ { 2 } \left( \frac { 1 } { 4 } \right) \frac { 1 } { \sqrt { 3 x - 4 } } ( 4 )$$
A) $\frac { 7 x ^ { 2 } - 8 } { \sqrt { 3 x - 4 } }$
B) $\frac { x ( 7 x - 4 ) } { \sqrt { 3 x - 4 } }$
C) $\frac { x ( 7 x - 8 ) } { \sqrt { 3 x - 4 } }$
D) $\frac { 7 x ^ { 2 } - 4 } { \sqrt { 3 x - 4 } }$

Question

Quizplus · Accepted Answer

The given expression can be simplified as follows: $$2x\sqrt{3x-4} + x^2\left(\frac{1}{4}\right)\frac{1}{\sqrt{3x-4}}(4) = 2x\sqrt{3x-4} + x^2\frac{4}{4\sqrt{3x-4}}$$$$= 2x\sqrt{3x-4} + \frac{x^2}{\sqrt{3x-4}} = \frac{2x(3x-4) + x^2}{\sqrt{3x-4}}$$$$= \frac{6x^2 - 8x + x^2}{\sqrt{3x-4}} = \frac{7x^2 - 8x}{\sqrt{3x-4}} = \frac{x(7x - 8)}{\sqrt{3x-4}}$$Therefore, the simplified expression is $\frac{x(7x - 8)}{\sqrt{3x - 4}}$, which matches choice C.

Simplify the Expression 2x3x−4+x2(14)13x−4(4)2 x \sqrt { 3 x - 4 } + x ^ { 2 } \left( \frac { 1 } { 4 } \right) \frac { 1 } { \sqrt { 3 x - 4 } } ( 4 )2x3x−4​+x2(41​)3x−4​1​(4)

Simplify the Expression $2 x \sqrt { 3 x - 4 } + x ^ { 2 } \left( \frac { 1 } { 4 } \right) \frac { 1 } { \sqrt { 3 x - 4 } } ( 4 )$