Mister Exam
How do you ((t^(2))/(3)+(8t)/(3))(2t+6) in partial fractions?
The solution
You have entered
[src]
/ 2 \ |t 8*t| |-- + ---|*(2*t + 6) \3 3 /
$$\left(2 t + 6\right) \left(\frac{t^{2}}{3} + \frac{8 t}{3}\right)$$
(t^2/3 + (8*t)/3)*(2*t + 6)
Factorization
[src]
(t + 8)*(t + 3)*t
$$t \left(t + 3\right) \left(t + 8\right)$$
((t + 8)*(t + 3))*t
Fraction decomposition
[src]
16*t + 2*t^3/3 + 22*t^2/3
$$\frac{2 t^{3}}{3} + \frac{22 t^{2}}{3} + 16 t$$
3 2
2*t 22*t
16*t + ---- + -----
3 3
General simplification
[src]
2*t*(3 + t)*(8 + t)
-------------------
3
$$\frac{2 t \left(t + 3\right) \left(t + 8\right)}{3}$$
2*t*(3 + t)*(8 + t)/3
Numerical answer
[src]
(6.0 + 2.0*t)*(0.333333333333333*t^2 + 2.66666666666667*t)
(6.0 + 2.0*t)*(0.333333333333333*t^2 + 2.66666666666667*t)
Combinatorics
[src]
2*t*(3 + t)*(8 + t)
-------------------
3
$$\frac{2 t \left(t + 3\right) \left(t + 8\right)}{3}$$
2*t*(3 + t)*(8 + t)/3
Combining rational expressions
[src]
2*t*(3 + t)*(8 + t)
-------------------
3
$$\frac{2 t \left(t + 3\right) \left(t + 8\right)}{3}$$
2*t*(3 + t)*(8 + t)/3
Rational denominator
[src]
/ 2 \
(6 + 2*t)*\t + 8*t/
--------------------
3
$$\frac{\left(2 t + 6\right) \left(t^{2} + 8 t\right)}{3}$$
(6 + 2*t)*(t^2 + 8*t)/3
Common denominator
[src]
3 2
2*t 22*t
16*t + ---- + -----
3 3
$$\frac{2 t^{3}}{3} + \frac{22 t^{2}}{3} + 16 t$$
16*t + 2*t^3/3 + 22*t^2/3