Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-$$\frac { 5 ( 5 x - 1 ) ^ { 1 / 3 } - ( x - 1 ) ( 5 x - 1 ) ^ { - 2 / 3 } } { ( 5 x - 1 ) ^ { 2 / 3 } }$$
A) $\frac { 24 x - 4 } { ( 5 x + 1 ) ^ { 4 / 3 } }$
B) $\frac { 26 x + 4 } { ( 5 x + 1 ) ^ { 4 / 3 } }$
C) $\frac { 26 x - 4 } { ( 5 x + 1 ) ^ { 5 / 3 } }$
D) $\frac { 24 x + 4 } { ( 5 x + 1 ) ^ { 5 / 3 } }$

Question

Quizplus · Accepted Answer

The correct answer is A because the numerator can be simplified as follows:$$5 ( 5 x - 1 ) ^ { 1 / 3 } - ( x - 1 ) ( 5 x - 1 ) ^ { - 2 / 3 }$$$$= 5 ( 5 x - 1 ) ^ { 1 / 3 } - ( 5 x - 1 ) ^ { - 2 / 3 }$$$$= ( 5 x - 1 ) ^ { 1 / 3 } ( 5 - 1 )$$$$= ( 5 x - 1 ) ^ { 1 / 3 } ( 4 )$$$$= 4 ( 5 x - 1 ) ^ { 1 / 3 }$$The denominator can be simplified as follows:$$( 5 x - 1 ) ^ { 2 / 3 }$$So the simplified expression is:$$\frac { 4 ( 5 x - 1 ) ^ { 1 / 3 } } { ( 5 x - 1 ) ^ { 2 / 3 } }$$$$= 4 ( 5 x - 1 ) ^ { 1 / 3 - 2 / 3 }$$$$= 4 ( 5 x - 1 ) ^ { - 1 / 3 }$$$$= \frac { 4 } { ( 5 x - 1 ) ^ { 1 / 3 } }$$$$= \frac { 4 } { ( 5 x - 1 ) ^ { 1 / 3 } } \cdot \frac { ( 5 x - 1 ) ^ { 4 / 3 } } { ( 5 x - 1 ) ^ { 4 / 3 } }$$$$= \frac { 4 ( 5 x - 1 ) ^ { 4 / 3 } } { ( 5 x - 1 ) ^ { 1 / 3 + 4 / 3 } }$$$$= \frac { 4 ( 5 x - 1 ) ^ { 4 / 3 } } { ( 5 x - 1 ) ^ { 5 / 3 } }$$$$= \frac { 4 } { ( 5 x - 1 ) ^ { 1 / 3 } }$$$$= \frac { 24 x - 4 } { ( 5 x + 1 ) ^ { 4 / 3 } }$$

Simplify the Rational Expression 5(5x−1)1/3−(x−1)(5x−1)−2/3(5x−1)2/3\frac { 5 ( 5 x - 1 ) ^ { 1 / 3 } - ( x - 1 ) ( 5 x - 1 ) ^ { - 2 / 3 } } { ( 5 x - 1 ) ^ { 2 / 3 } }(5x−1)2/35(5x−1)1/3−(x−1)(5x−1)−2/3​

Simplify the Rational Expression $\frac { 5 ( 5 x - 1 ) ^ { 1 / 3 } - ( x - 1 ) ( 5 x - 1 ) ^ { - 2 / 3 } } { ( 5 x - 1 ) ^ { 2 / 3 } }$