Mister Exam
Expression simplification/
Least common denominator/
(234/(((7/20)*p+1)*(p+1)*((111/10)*p+1)))*((3/10)+10/p)
Least common denominator (234/(((7/20)*p+1)*(p+1)*((111/10)*p+1)))*((3/10)+10/p)
The solution
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234 /3 10\ -----------------------------*|-- + --| /7*p \ /111*p \ \10 p / |--- + 1|*(p + 1)*|----- + 1| \ 20 / \ 10 /
$$\frac{234}{\left(\frac{7 p}{20} + 1\right) \left(p + 1\right) \left(\frac{111 p}{10} + 1\right)} \left(\frac{3}{10} + \frac{10}{p}\right)$$
(234/((((7*p/20 + 1)*(p + 1))*(111*p/10 + 1))))*(3/10 + 10/p)
General simplification
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4680*(100 + 3*p) --------------------------------- p*(1 + p)*(10 + 111*p)*(20 + 7*p)
$$\frac{4680 \left(3 p + 100\right)}{p \left(p + 1\right) \left(7 p + 20\right) \left(111 p + 10\right)}$$
4680*(100 + 3*p)/(p*(1 + p)*(10 + 111*p)*(20 + 7*p))
Fraction decomposition
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2340/p - 6383214396/(21715*(10 + 111*p)) - 56448/(215*(20 + 7*p)) + 34920/(101*(1 + p))
$$- \frac{6383214396}{21715 \left(111 p + 10\right)} - \frac{56448}{215 \left(7 p + 20\right)} + \frac{34920}{101 \left(p + 1\right)} + \frac{2340}{p}$$
2340 6383214396 56448 34920 ---- - ------------------ - -------------- + ----------- p 21715*(10 + 111*p) 215*(20 + 7*p) 101*(1 + p)
Common denominator
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468000 + 14040*p
----------------------------------
4 2 3
200*p + 777*p + 2490*p + 3067*p
$$\frac{14040 p + 468000}{777 p^{4} + 3067 p^{3} + 2490 p^{2} + 200 p}$$
(468000 + 14040*p)/(200*p + 777*p^4 + 2490*p^2 + 3067*p^3)
Assemble expression
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/3 10\
234*|-- + --|
\10 p /
-----------------------------
/ 7*p\ / 111*p\
(1 + p)*|1 + ---|*|1 + -----|
\ 20/ \ 10 /
$$\frac{234 \left(\frac{3}{10} + \frac{10}{p}\right)}{\left(\frac{7 p}{20} + 1\right) \left(p + 1\right) \left(\frac{111 p}{10} + 1\right)}$$
234*(3/10 + 10/p)/((1 + p)*(1 + 7*p/20)*(1 + 111*p/10))
Trigonometric part
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/3 10\
234*|-- + --|
\10 p /
-----------------------------
/ 7*p\ / 111*p\
(1 + p)*|1 + ---|*|1 + -----|
\ 20/ \ 10 /
$$\frac{234 \left(\frac{3}{10} + \frac{10}{p}\right)}{\left(\frac{7 p}{20} + 1\right) \left(p + 1\right) \left(\frac{111 p}{10} + 1\right)}$$
234*(3/10 + 10/p)/((1 + p)*(1 + 7*p/20)*(1 + 111*p/10))
Rational denominator
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4680000 + 140400*p ------------------------------------ 10*p*(1 + p)*(10 + 111*p)*(20 + 7*p)
$$\frac{140400 p + 4680000}{10 p \left(p + 1\right) \left(7 p + 20\right) \left(111 p + 10\right)}$$
(4680000 + 140400*p)/(10*p*(1 + p)*(10 + 111*p)*(20 + 7*p))
Combining rational expressions
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4680*(100 + 3*p) --------------------------------- p*(1 + p)*(10 + 111*p)*(20 + 7*p)
$$\frac{4680 \left(3 p + 100\right)}{p \left(p + 1\right) \left(7 p + 20\right) \left(111 p + 10\right)}$$
4680*(100 + 3*p)/(p*(1 + p)*(10 + 111*p)*(20 + 7*p))
Numerical answer
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234.0*(0.3 + 10.0/p)/((1.0 + p)*(1.0 + 0.35*p)*(1.0 + 11.1*p))
234.0*(0.3 + 10.0/p)/((1.0 + p)*(1.0 + 0.35*p)*(1.0 + 11.1*p))
Combinatorics
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4680*(100 + 3*p) --------------------------------- p*(1 + p)*(10 + 111*p)*(20 + 7*p)
$$\frac{4680 \left(3 p + 100\right)}{p \left(p + 1\right) \left(7 p + 20\right) \left(111 p + 10\right)}$$
4680*(100 + 3*p)/(p*(1 + p)*(10 + 111*p)*(20 + 7*p))
Powers
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/3 10\
234*|-- + --|
\10 p /
-----------------------------
/ 7*p\ / 111*p\
(1 + p)*|1 + ---|*|1 + -----|
\ 20/ \ 10 /
$$\frac{234 \left(\frac{3}{10} + \frac{10}{p}\right)}{\left(\frac{7 p}{20} + 1\right) \left(p + 1\right) \left(\frac{111 p}{10} + 1\right)}$$
351 2340
--- + ----
5 p
-----------------------------
/ 7*p\ / 111*p\
(1 + p)*|1 + ---|*|1 + -----|
\ 20/ \ 10 /
$$\frac{\frac{351}{5} + \frac{2340}{p}}{\left(\frac{7 p}{20} + 1\right) \left(p + 1\right) \left(\frac{111 p}{10} + 1\right)}$$
(351/5 + 2340/p)/((1 + p)*(1 + 7*p/20)*(1 + 111*p/10))