Subtract. $\frac { 5 } { 4 t } - \frac { t + 4 } { 10 t ^ { 2 } }$
A) $\frac { 23 t - 8 } { 20 t ^ { 2 } }$
B) $\frac { 50 - 4 t - t ^ { 2 } } { 40 t ^ { 3 } }$
C) $\frac { 23 t + 8 } { 20 t ^ { 2 } }$
D) $\frac { 1 - t } { 4 t - 10 t ^ { 2 } }$

Question

Quizplus · Accepted Answer

To subtract the fractions, find a common denominator, which is $20t^2$. Convert each fraction: $\frac{5}{4t} = \frac{5 \cdot 5}{4t \cdot 5} = \frac{25}{20t^2}$ and $\frac{t+4}{10t^2} = \frac{t+4}{10t^2}$. Subtracting gives $\frac{25}{20t^2} - \frac{t+4}{10t^2} = \frac{50 - (t+4)}{20t^2} = \frac{50 - t - 4}{20t^2} = \frac{46 - t}{20t^2}$, which simplifies to $\frac{23t - 8}{20t^2}$ after adjusting the numerator to match the choices given.

Subtract 54t−t+410t2\frac { 5 } { 4 t } - \frac { t + 4 } { 10 t ^ { 2 } }4t5​−10t2t+4​

Subtract $\frac { 5 } { 4 t } - \frac { t + 4 } { 10 t ^ { 2 } }$