Mister Exam

# How do you (5/s)*(2/((1/5)*s+1))*(1/(s+1)) in partial fractions?

An expression to simplify:

### The solution

You have entered [src]
5   2
-*-----
s s
- + 1
5
-------
s + 1 
$$\frac{\frac{5}{s} \frac{2}{\frac{s}{5} + 1}}{s + 1}$$
((5/s)*(2/(s/5 + 1)))/(s + 1)
Fraction decomposition [src]
10/s - 25/(2*(1 + s)) + 5/(2*(5 + s))
$$\frac{5}{2 \left(s + 5\right)} - \frac{25}{2 \left(s + 1\right)} + \frac{10}{s}$$
10       25          5
-- - --------- + ---------
s    2*(1 + s)   2*(5 + s)
General simplification [src]
        50
-----------------
s*(1 + s)*(5 + s)
$$\frac{50}{s \left(s + 1\right) \left(s + 5\right)}$$
50/(s*(1 + s)*(5 + s))
10.0/(s*(1.0 + s)*(1.0 + 0.2*s))
10.0/(s*(1.0 + s)*(1.0 + 0.2*s))
Powers [src]
        10
-----------------
/    s\
s*(1 + s)*|1 + -|
\    5/
$$\frac{10}{s \left(\frac{s}{5} + 1\right) \left(s + 1\right)}$$
10/(s*(1 + s)*(1 + s/5))
Combining rational expressions [src]
        50
-----------------
s*(1 + s)*(5 + s)
$$\frac{50}{s \left(s + 1\right) \left(s + 5\right)}$$
50/(s*(1 + s)*(5 + s))
Rational denominator [src]
        50
-----------------
s*(1 + s)*(5 + s)
$$\frac{50}{s \left(s + 1\right) \left(s + 5\right)}$$
50/(s*(1 + s)*(5 + s))
Assemble expression [src]
        10
-----------------
/    s\
s*(1 + s)*|1 + -|
\    5/
$$\frac{10}{s \left(\frac{s}{5} + 1\right) \left(s + 1\right)}$$
10/(s*(1 + s)*(1 + s/5))
Common denominator [src]
       50
---------------
3            2
s  + 5*s + 6*s 
$$\frac{50}{s^{3} + 6 s^{2} + 5 s}$$
50/(s^3 + 5*s + 6*s^2)
Trigonometric part [src]
        10
-----------------
/    s\
s*(1 + s)*|1 + -|
\    5/
$$\frac{10}{s \left(\frac{s}{5} + 1\right) \left(s + 1\right)}$$
10/(s*(1 + s)*(1 + s/5))
Combinatorics [src]
        50
-----------------
s*(1 + s)*(5 + s)
$$\frac{50}{s \left(s + 1\right) \left(s + 5\right)}$$
50/(s*(1 + s)*(5 + s))