Mister Exam
Expression simplification/
Least common denominator/
((-k2/p)*(k3/(t3*p+1))+k1*p)*((k5*p)/(1+k3*p*(k3/(t3*p+1))*(k4*(t4*p+1))))
Least common denominator ((-k2/p)*(k3/(t3*p+1))+k1*p)*((k5*p)/(1+k3*p*(k3/(t3*p+1))*(k4*(t4*p+1))))
The solution
You have entered
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/-k2 k3 \ k5*p
|----*-------- + k1*p|*-------------------------------
\ p t3*p + 1 / k3
1 + k3*p*--------*k4*(t4*p + 1)
t3*p + 1
$$\frac{k_{5} p}{k_{4} \left(p t_{4} + 1\right) k_{3} p \frac{k_{3}}{p t_{3} + 1} + 1} \left(k_{1} p + \frac{\left(-1\right) k_{2}}{p} \frac{k_{3}}{p t_{3} + 1}\right)$$
(((-k2)/p)*(k3/(t3*p + 1)) + k1*p)*((k5*p)/(1 + ((k3*p)*(k3/(t3*p + 1)))*(k4*(t4*p + 1))))
General simplification
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/ 2 \
k5*\-k2*k3 + k1*p *(1 + p*t3)/
------------------------------
2
1 + p*t3 + k4*p*k3 *(1 + p*t4)
$$\frac{k_{5} \left(k_{1} p^{2} \left(p t_{3} + 1\right) - k_{2} k_{3}\right)}{k_{3}^{2} k_{4} p \left(p t_{4} + 1\right) + p t_{3} + 1}$$
k5*(-k2*k3 + k1*p^2*(1 + p*t3))/(1 + p*t3 + k4*p*k3^2*(1 + p*t4))
Combining rational expressions
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/ 2 \
k5*\-k2*k3 + k1*p *(1 + p*t3)/
------------------------------
2
1 + p*t3 + k4*p*k3 *(1 + p*t4)
$$\frac{k_{5} \left(k_{1} p^{2} \left(p t_{3} + 1\right) - k_{2} k_{3}\right)}{k_{3}^{2} k_{4} p \left(p t_{4} + 1\right) + p t_{3} + 1}$$
k5*(-k2*k3 + k1*p^2*(1 + p*t3))/(1 + p*t3 + k4*p*k3^2*(1 + p*t4))
Trigonometric part
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/ k2*k3 \
k5*p*|k1*p - ------------|
\ p*(1 + p*t3)/
--------------------------
2
k4*p*k3 *(1 + p*t4)
1 + -------------------
1 + p*t3
$$\frac{k_{5} p \left(k_{1} p - \frac{k_{2} k_{3}}{p \left(p t_{3} + 1\right)}\right)}{\frac{k_{3}^{2} k_{4} p \left(p t_{4} + 1\right)}{p t_{3} + 1} + 1}$$
k5*p*(k1*p - k2*k3/(p*(1 + p*t3)))/(1 + k4*p*k3^2*(1 + p*t4)/(1 + p*t3))
Rational denominator
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/ 2 3\
k5*\k1*p - k2*k3 + k1*t3*p /
----------------------------------
2 2 2
1 + p*t3 + k4*p*k3 + k4*t4*k3 *p
$$\frac{k_{5} \left(k_{1} p^{3} t_{3} + k_{1} p^{2} - k_{2} k_{3}\right)}{k_{3}^{2} k_{4} p^{2} t_{4} + k_{3}^{2} k_{4} p + p t_{3} + 1}$$
k5*(k1*p^2 - k2*k3 + k1*t3*p^3)/(1 + p*t3 + k4*p*k3^2 + k4*t4*k3^2*p^2)
Combinatorics
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/ 2 3\
k5*\k1*p - k2*k3 + k1*t3*p /
----------------------------------
2 2 2
1 + p*t3 + k4*p*k3 + k4*t4*k3 *p
$$\frac{k_{5} \left(k_{1} p^{3} t_{3} + k_{1} p^{2} - k_{2} k_{3}\right)}{k_{3}^{2} k_{4} p^{2} t_{4} + k_{3}^{2} k_{4} p + p t_{3} + 1}$$
k5*(k1*p^2 - k2*k3 + k1*t3*p^3)/(1 + p*t3 + k4*p*k3^2 + k4*t4*k3^2*p^2)
Numerical answer
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k5*p*(k1*p - k2*k3/(p*(1.0 + p*t3)))/(1.0 + k4*p*k3^2*(1.0 + p*t4)/(1.0 + p*t3))
k5*p*(k1*p - k2*k3/(p*(1.0 + p*t3)))/(1.0 + k4*p*k3^2*(1.0 + p*t4)/(1.0 + p*t3))
Powers
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/ k2*k3 \
k5*p*|k1*p - ------------|
\ p*(1 + p*t3)/
--------------------------
2
k4*p*k3 *(1 + p*t4)
1 + -------------------
1 + p*t3
$$\frac{k_{5} p \left(k_{1} p - \frac{k_{2} k_{3}}{p \left(p t_{3} + 1\right)}\right)}{\frac{k_{3}^{2} k_{4} p \left(p t_{4} + 1\right)}{p t_{3} + 1} + 1}$$
k5*p*(k1*p - k2*k3/(p*(1 + p*t3)))/(1 + k4*p*k3^2*(1 + p*t4)/(1 + p*t3))
Common denominator
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2 3
k1*k5*p - k2*k3*k5 + k1*k5*t3*p
----------------------------------
2 2 2
1 + p*t3 + k4*p*k3 + k4*t4*k3 *p
$$\frac{k_{1} k_{5} p^{3} t_{3} + k_{1} k_{5} p^{2} - k_{2} k_{3} k_{5}}{k_{3}^{2} k_{4} p^{2} t_{4} + k_{3}^{2} k_{4} p + p t_{3} + 1}$$
(k1*k5*p^2 - k2*k3*k5 + k1*k5*t3*p^3)/(1 + p*t3 + k4*p*k3^2 + k4*t4*k3^2*p^2)
Assemble expression
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/ k2*k3 \
k5*p*|k1*p - ------------|
\ p*(1 + p*t3)/
--------------------------
2
k4*p*k3 *(1 + p*t4)
1 + -------------------
1 + p*t3
$$\frac{k_{5} p \left(k_{1} p - \frac{k_{2} k_{3}}{p \left(p t_{3} + 1\right)}\right)}{\frac{k_{3}^{2} k_{4} p \left(p t_{4} + 1\right)}{p t_{3} + 1} + 1}$$
k5*p*(k1*p - k2*k3/(p*(1 + p*t3)))/(1 + k4*p*k3^2*(1 + p*t4)/(1 + p*t3))