Perform the indicated operation involving rational expressions. $\frac { 7 t ^ { 5 } - 21 t ^ { 4 } } { t ^ { 3 } - 3 t ^ { 2 } } \cdot \frac { t ^ { 2 } - 6 t + 9 } { t ^ { 5 } - 9 t ^ { 3 } }$
A) $\frac { 7 t - 21 } { t ^ { 2 } + 3 t }$
B) $\frac { t - 3 } { t ^ { 2 } + 3 t }$
C) $\frac { 7 } { t ^ { 2 } + 3 t }$
D) $\frac { 7 t ^ { 2 } + 21 } { t ^ { 2 } + 3 t }$

Question

Quizplus · Accepted Answer

The correct answer is A because the numerator of the first fraction is multiplied by the numerator of the second fraction, and the denominator of the first fraction is multiplied by the denominator of the second fraction. This gives $\frac { 7 t ^ { 5 } - 21 t ^ { 4 } } { t ^ { 3 } - 3 t ^ { 2 } } \cdot \frac { t ^ { 2 } - 6 t + 9 } { t ^ { 5 } - 9 t ^ { 3 } } = \frac { 7 t ^ { 5 } - 21 t ^ { 4 } } { t ^ { 3 } - 3 t ^ { 2 } } \cdot \frac { ( t - 3 ) ^ { 2 } } { t ^ { 3 } ( t ^ { 2 } - 9 ) } = \frac { 7 t ^ { 5 } - 21 t ^ { 4 } } { t ^ { 3 } - 3 t ^ { 2 } } \cdot \frac { ( t - 3 ) ^ { 2 } } { t ^ { 3 } ( t - 3 ) ( t + 3 ) } = \frac { 7 t ^ { 5 } - 21 t ^ { 4 } } { t ^ { 3 } - 3 t ^ { 2 } } \cdot \frac { t - 3 } { t ^ { 3 } ( t + 3 ) } = \frac { 7 t ^ { 2 } - 21 t } { t ^ { 2 } + 3 t }$

Perform the Indicated Operation Involving Rational Expressions 7t5−21t4t3−3t2⋅t2−6t+9t5−9t3\frac { 7 t ^ { 5 } - 21 t ^ { 4 } } { t ^ { 3 } - 3 t ^ { 2 } } \cdot \frac { t ^ { 2 } - 6 t + 9 } { t ^ { 5 } - 9 t ^ { 3 } }t3−3t27t5−21t4​⋅t5−9t3t2−6t+9​

Perform the Indicated Operation Involving Rational Expressions $\frac { 7 t ^ { 5 } - 21 t ^ { 4 } } { t ^ { 3 } - 3 t ^ { 2 } } \cdot \frac { t ^ { 2 } - 6 t + 9 } { t ^ { 5 } - 9 t ^ { 3 } }$