Mister Exam
How do you (5/s)*(2/((1/5)*s+1))*(1/(s+1)) in partial fractions?
The solution
You have entered
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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
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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
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50 ----------------- s*(1 + s)*(5 + s)
$$\frac{50}{s \left(s + 1\right) \left(s + 5\right)}$$
50/(s*(1 + s)*(5 + s))
Powers
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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
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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
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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
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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
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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
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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
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50 ----------------- s*(1 + s)*(5 + s)
$$\frac{50}{s \left(s + 1\right) \left(s + 5\right)}$$
50/(s*(1 + s)*(5 + s))