Mister Exam

# Least common denominator (k1*p*(k4*(t4*p+1))+k2/p)*k5*p+(k1*p)*(k3/(t3*p+1))

An expression to simplify:

### The solution

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