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Least common denominator:
x^2+25/x-5-10*x/x-5
k1/(1+k1*(-k2*k3*k3/((t3^2*s^2+2*t3*s*e+1)*(t2*s+1))+1/(t1*s+1)))
n*((1+p)^k+p^k*log(p)+(1+p)^k*(k+1)*log(1+p))/k-n*(p^k+(k+1)*(1+p)^k)/k^2
(k1*p*(k4*(t4*p+1))+k2/p)*k5*p+(k1*p)*(k3/(t3*p+1))
Factor polynomial:
m^2-a^2
x^4-9
x^3-y^3
m^3+m^2+m+1-m^4-m^3-m^2-m-1
Factor squared:
-y^4-y^2+3
y^4+y^2+7
-y^4+y^2+7
x^2-9*x+5
How do you in partial fractions?:
(t^4+9)/(t^4+9t^2)
(x^2+2x-15)/(x+5)
3*x^2/(8-x^4)+4*x^6/(8-x^4)^2
1/(n*(n+1)*(n+2))
Identical expressions
k one /(one +k one *(-k two *k3*k3/((t3^ two *s^ two +2*t3*s*e+ one)*(t2*s+ one))+1/(t1*s+1)))
k1 divide by (1 plus k1 multiply by ( minus k2 multiply by k3 multiply by k3 divide by ((t3 squared multiply by s squared plus 2 multiply by t3 multiply by s multiply by e plus 1) multiply by (t2 multiply by s plus 1)) plus 1 divide by (t1 multiply by s plus 1)))
k one divide by (one plus k one multiply by ( minus k two multiply by k3 multiply by k3 divide by ((t3 to the power of two multiply by s to the power of two plus 2 multiply by t3 multiply by s multiply by e plus one) multiply by (t2 multiply by s plus one)) plus 1 divide by (t1 multiply by s plus 1)))
k1/(1+k1*(-k2*k3*k3/((t32*s2+2*t3*s*e+1)*(t2*s+1))+1/(t1*s+1)))
k1/1+k1*-k2*k3*k3/t32*s2+2*t3*s*e+1*t2*s+1+1/t1*s+1
k1/(1+k1*(-k2*k3*k3/((t3²*s²+2*t3*s*e+1)*(t2*s+1))+1/(t1*s+1)))
k1/(1+k1*(-k2*k3*k3/((t3 to the power of 2*s to the power of 2+2*t3*s*e+1)*(t2*s+1))+1/(t1*s+1)))
k1/(1+k1(-k2k3k3/((t3^2s^2+2t3se+1)(t2s+1))+1/(t1s+1)))
k1/(1+k1(-k2k3k3/((t32s2+2t3se+1)(t2s+1))+1/(t1s+1)))
k1/1+k1-k2k3k3/t32s2+2t3se+1t2s+1+1/t1s+1
k1/1+k1-k2k3k3/t3^2s^2+2t3se+1t2s+1+1/t1s+1
k1 divide by (1+k1*(-k2*k3*k3 divide by ((t3^2*s^2+2*t3*s*e+1)*(t2*s+1))+1 divide by (t1*s+1)))
Similar expressions
k1/(1+k1*(-k2*k3*k3/((t3^2*s^2+2*t3*s*e+1)*(t2*s-1))+1/(t1*s+1)))
k1/(1+k1*(-k2*k3*k3/((t3^2*s^2-2*t3*s*e+1)*(t2*s+1))+1/(t1*s+1)))
k1/(1+k1*(-k2*k3*k3/((t3^2*s^2+2*t3*s*e+1)*(t2*s+1))+1/(t1*s-1)))
k1/(1+k1*(-k2*k3*k3/((t3^2*s^2+2*t3*s*e-1)*(t2*s+1))+1/(t1*s+1)))
k1/(1+k1*(-k2*k3*k3/((t3^2*s^2+2*t3*s*e+1)*(t2*s+1))-1/(t1*s+1)))
k1/(1-k1*(-k2*k3*k3/((t3^2*s^2+2*t3*s*e+1)*(t2*s+1))+1/(t1*s+1)))
k1/(1+k1*(k2*k3*k3/((t3^2*s^2+2*t3*s*e+1)*(t2*s+1))+1/(t1*s+1)))

Expression simplification/ Least common denominator/ k1/(1+k1*(-k2*k3*k3/((t3^2*s^2+2*t3*s*e+1)*(t2*s+1))+1/(t1*s+1)))

Least common denominator k1/(1+k1(-k2k3k3/((t3^2s^2+2t3se+1)(t2s+1))+1/(t1s+1)))

The solution

You have entered [src]

                          k1                          
------------------------------------------------------
       /            -k2*k3*k3                   1    \
1 + k1*|---------------------------------- + --------|
       |/  2  2               \              t1*s + 1|
       \\t3 *s  + 2*t3*s*E + 1/*(t2*s + 1)           /

$$\frac{k_{1}}{k_{1} \left(\frac{k_{3} \cdot - k_{2} k_{3}}{\left(s t_{2} + 1\right) \left(\left(s^{2} t_{3}^{2} + e s 2 t_{3}\right) + 1\right)} + \frac{1}{s t_{1} + 1}\right) + 1}$$

k1/(1 + k1*((((-k2)*k3)*k3)/(((t3^2*s^2 + ((2*t3)*s)*E + 1)*(t2*s + 1))) + 1/(t1*s + 1)))

General simplification [src]

                          k1                          
------------------------------------------------------
       /                              2              \
       |   1                     k2*k3               |
1 + k1*|-------- - ----------------------------------|
       |1 + s*t1              /     2   2           \|
       \           (1 + s*t2)*\1 + s *t3  + 2*E*s*t3//

$$\frac{k_{1}}{k_{1} \left(- \frac{k_{2} k_{3}^{2}}{\left(s t_{2} + 1\right) \left(s^{2} t_{3}^{2} + 2 e s t_{3} + 1\right)} + \frac{1}{s t_{1} + 1}\right) + 1}$$

k1/(1 + k1*(1/(1 + s*t1) - k2*k3^2/((1 + s*t2)*(1 + s^2*t3^2 + 2*E*s*t3))))

Expand expression [src]

                          k1                          
------------------------------------------------------
       /                              2              \
       |   1                     k2*k3               |
1 + k1*|-------- - ----------------------------------|
       |t1*s + 1              /  2  2               \|
       \           (t2*s + 1)*\t3 *s  + 2*t3*s*E + 1//

$$\frac{k_{1}}{k_{1} \left(- \frac{k_{2} k_{3}^{2}}{\left(s t_{2} + 1\right) \left(\left(s^{2} t_{3}^{2} + e s 2 t_{3}\right) + 1\right)} + \frac{1}{s t_{1} + 1}\right) + 1}$$

k1/(1 + k1*(1/(t1*s + 1) - k2*k3^2/((t2*s + 1)*(t3^2*s^2 + ((2*t3)*s)*E + 1))))

Numerical answer [src]

k1/(1.0 + k1*(1/(1.0 + s*t1) - k2*k3^2/((1.0 + s*t2)*(1.0 + s^2*t3^2 + 5.43656365691809*s*t3))))

k1/(1.0 + k1*(1/(1.0 + s*t1) - k2*k3^2/((1.0 + s*t2)*(1.0 + s^2*t3^2 + 5.43656365691809*s*t3))))

Combining rational expressions [src]

                              k1*(1 + s*t1)*(1 + s*t2)*(1 + s*t3*(2*E + s*t3))                             
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   /                                          2           \                                                
k1*\(1 + s*t2)*(1 + s*t3*(2*E + s*t3)) - k2*k3 *(1 + s*t1)/ + (1 + s*t1)*(1 + s*t2)*(1 + s*t3*(2*E + s*t3))

$$\frac{k_{1} \left(s t_{1} + 1\right) \left(s t_{2} + 1\right) \left(s t_{3} \left(s t_{3} + 2 e\right) + 1\right)}{k_{1} \left(- k_{2} k_{3}^{2} \left(s t_{1} + 1\right) + \left(s t_{2} + 1\right) \left(s t_{3} \left(s t_{3} + 2 e\right) + 1\right)\right) + \left(s t_{1} + 1\right) \left(s t_{2} + 1\right) \left(s t_{3} \left(s t_{3} + 2 e\right) + 1\right)}$$

k1*(1 + s*t1)*(1 + s*t2)*(1 + s*t3*(2*E + s*t3))/(k1*((1 + s*t2)*(1 + s*t3*(2*E + s*t3)) - k2*k3^2*(1 + s*t1)) + (1 + s*t1)*(1 + s*t2)*(1 + s*t3*(2*E + s*t3)))

Combinatorics [src]

                                                                                                                       /     2   2           \                                                                                              
                                                                                              k1*(1 + s*t1)*(1 + s*t2)*\1 + s *t3  + 2*E*s*t3/                                                                                              
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                        2   2                 2   2          2       3   2       3   2           2                     3   2          4   2                            2              2                2                 2                 3
1 + k1 + s*t1 + s*t2 + s *t3  + k1*s*t2 + k1*s *t3  + t1*t2*s  + t1*s *t3  + t2*s *t3  - k1*k2*k3  + 2*E*s*t3 + k1*t2*s *t3  + t1*t2*s *t3  + 2*E*k1*s*t3 + 2*E*t1*t3*s  + 2*E*t2*t3*s  - k1*k2*s*t1*k3  + 2*E*k1*t2*t3*s  + 2*E*t1*t2*t3*s

$$\frac{k_{1} \left(s t_{1} + 1\right) \left(s t_{2} + 1\right) \left(s^{2} t_{3}^{2} + 2 e s t_{3} + 1\right)}{- k_{1} k_{2} k_{3}^{2} s t_{1} - k_{1} k_{2} k_{3}^{2} + k_{1} s^{3} t_{2} t_{3}^{2} + 2 e k_{1} s^{2} t_{2} t_{3} + k_{1} s^{2} t_{3}^{2} + k_{1} s t_{2} + 2 e k_{1} s t_{3} + k_{1} + s^{4} t_{1} t_{2} t_{3}^{2} + 2 e s^{3} t_{1} t_{2} t_{3} + s^{3} t_{1} t_{3}^{2} + s^{3} t_{2} t_{3}^{2} + s^{2} t_{1} t_{2} + 2 e s^{2} t_{1} t_{3} + 2 e s^{2} t_{2} t_{3} + s^{2} t_{3}^{2} + s t_{1} + s t_{2} + 2 e s t_{3} + 1}$$

k1*(1 + s*t1)*(1 + s*t2)*(1 + s^2*t3^2 + 2*E*s*t3)/(1 + k1 + s*t1 + s*t2 + s^2*t3^2 + k1*s*t2 + k1*s^2*t3^2 + t1*t2*s^2 + t1*s^3*t3^2 + t2*s^3*t3^2 - k1*k2*k3^2 + 2*E*s*t3 + k1*t2*s^3*t3^2 + t1*t2*s^4*t3^2 + 2*E*k1*s*t3 + 2*E*t1*t3*s^2 + 2*E*t2*t3*s^2 - k1*k2*s*t1*k3^2 + 2*E*k1*t2*t3*s^2 + 2*E*t1*t2*t3*s^3)

Rational denominator [src]

                                                    /                   2   2          2       3   2       3   2                     4   2              2              2                 3\                                                 
                                                 k1*\1 + s*t1 + s*t2 + s *t3  + t1*t2*s  + t1*s *t3  + t2*s *t3  + 2*E*s*t3 + t1*t2*s *t3  + 2*E*t1*t3*s  + 2*E*t2*t3*s  + 2*E*t1*t2*t3*s /                                                 
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                        2   2                 2   2          2       3   2       3   2           2                     3   2          4   2                            2              2                2                 2                 3
1 + k1 + s*t1 + s*t2 + s *t3  + k1*s*t2 + k1*s *t3  + t1*t2*s  + t1*s *t3  + t2*s *t3  - k1*k2*k3  + 2*E*s*t3 + k1*t2*s *t3  + t1*t2*s *t3  + 2*E*k1*s*t3 + 2*E*t1*t3*s  + 2*E*t2*t3*s  - k1*k2*s*t1*k3  + 2*E*k1*t2*t3*s  + 2*E*t1*t2*t3*s

$$\frac{k_{1} \left(s^{4} t_{1} t_{2} t_{3}^{2} + 2 e s^{3} t_{1} t_{2} t_{3} + s^{3} t_{1} t_{3}^{2} + s^{3} t_{2} t_{3}^{2} + s^{2} t_{1} t_{2} + 2 e s^{2} t_{1} t_{3} + 2 e s^{2} t_{2} t_{3} + s^{2} t_{3}^{2} + s t_{1} + s t_{2} + 2 e s t_{3} + 1\right)}{- k_{1} k_{2} k_{3}^{2} s t_{1} - k_{1} k_{2} k_{3}^{2} + k_{1} s^{3} t_{2} t_{3}^{2} + 2 e k_{1} s^{2} t_{2} t_{3} + k_{1} s^{2} t_{3}^{2} + k_{1} s t_{2} + 2 e k_{1} s t_{3} + k_{1} + s^{4} t_{1} t_{2} t_{3}^{2} + 2 e s^{3} t_{1} t_{2} t_{3} + s^{3} t_{1} t_{3}^{2} + s^{3} t_{2} t_{3}^{2} + s^{2} t_{1} t_{2} + 2 e s^{2} t_{1} t_{3} + 2 e s^{2} t_{2} t_{3} + s^{2} t_{3}^{2} + s t_{1} + s t_{2} + 2 e s t_{3} + 1}$$

k1*(1 + s*t1 + s*t2 + s^2*t3^2 + t1*t2*s^2 + t1*s^3*t3^2 + t2*s^3*t3^2 + 2*E*s*t3 + t1*t2*s^4*t3^2 + 2*E*t1*t3*s^2 + 2*E*t2*t3*s^2 + 2*E*t1*t2*t3*s^3)/(1 + k1 + s*t1 + s*t2 + s^2*t3^2 + k1*s*t2 + k1*s^2*t3^2 + t1*t2*s^2 + t1*s^3*t3^2 + t2*s^3*t3^2 - k1*k2*k3^2 + 2*E*s*t3 + k1*t2*s^3*t3^2 + t1*t2*s^4*t3^2 + 2*E*k1*s*t3 + 2*E*t1*t3*s^2 + 2*E*t2*t3*s^2 - k1*k2*s*t1*k3^2 + 2*E*k1*t2*t3*s^2 + 2*E*t1*t2*t3*s^3)

Powers [src]

                          k1                          
------------------------------------------------------
       /                              2              \
       |   1                     k2*k3               |
1 + k1*|-------- - ----------------------------------|
       |1 + s*t1              /     2   2           \|
       \           (1 + s*t2)*\1 + s *t3  + 2*E*s*t3//

$$\frac{k_{1}}{k_{1} \left(- \frac{k_{2} k_{3}^{2}}{\left(s t_{2} + 1\right) \left(s^{2} t_{3}^{2} + 2 e s t_{3} + 1\right)} + \frac{1}{s t_{1} + 1}\right) + 1}$$

k1/(1 + k1*(1/(1 + s*t1) - k2*k3^2/((1 + s*t2)*(1 + s^2*t3^2 + 2*E*s*t3))))

Common denominator [src]

                                                                       2          2     2  2   2        2   2        2  3   2              2             2   2               2  2                                                                
                                                                     k1  + s*t2*k1  + k1 *s *t3  - k2*k1 *k3  + t2*k1 *s *t3  + 2*E*s*t3*k1  - k2*s*t1*k1 *k3  + 2*E*t2*t3*k1 *s                                                                 
k1 - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                             2   2                 2   2          2       3   2       3   2           2                     3   2          4   2                            2              2                2                 2                 3
     1 + k1 + s*t1 + s*t2 + s *t3  + k1*s*t2 + k1*s *t3  + t1*t2*s  + t1*s *t3  + t2*s *t3  - k1*k2*k3  + 2*E*s*t3 + k1*t2*s *t3  + t1*t2*s *t3  + 2*E*k1*s*t3 + 2*E*t1*t3*s  + 2*E*t2*t3*s  - k1*k2*s*t1*k3  + 2*E*k1*t2*t3*s  + 2*E*t1*t2*t3*s

$$k_{1} - \frac{- k_{1}^{2} k_{2} k_{3}^{2} s t_{1} - k_{1}^{2} k_{2} k_{3}^{2} + k_{1}^{2} s^{3} t_{2} t_{3}^{2} + 2 e k_{1}^{2} s^{2} t_{2} t_{3} + k_{1}^{2} s^{2} t_{3}^{2} + k_{1}^{2} s t_{2} + 2 e k_{1}^{2} s t_{3} + k_{1}^{2}}{- k_{1} k_{2} k_{3}^{2} s t_{1} - k_{1} k_{2} k_{3}^{2} + k_{1} s^{3} t_{2} t_{3}^{2} + 2 e k_{1} s^{2} t_{2} t_{3} + k_{1} s^{2} t_{3}^{2} + k_{1} s t_{2} + 2 e k_{1} s t_{3} + k_{1} + s^{4} t_{1} t_{2} t_{3}^{2} + 2 e s^{3} t_{1} t_{2} t_{3} + s^{3} t_{1} t_{3}^{2} + s^{3} t_{2} t_{3}^{2} + s^{2} t_{1} t_{2} + 2 e s^{2} t_{1} t_{3} + 2 e s^{2} t_{2} t_{3} + s^{2} t_{3}^{2} + s t_{1} + s t_{2} + 2 e s t_{3} + 1}$$

k1 - (k1^2 + s*t2*k1^2 + k1^2*s^2*t3^2 - k2*k1^2*k3^2 + t2*k1^2*s^3*t3^2 + 2*E*s*t3*k1^2 - k2*s*t1*k1^2*k3^2 + 2*E*t2*t3*k1^2*s^2)/(1 + k1 + s*t1 + s*t2 + s^2*t3^2 + k1*s*t2 + k1*s^2*t3^2 + t1*t2*s^2 + t1*s^3*t3^2 + t2*s^3*t3^2 - k1*k2*k3^2 + 2*E*s*t3 + k1*t2*s^3*t3^2 + t1*t2*s^4*t3^2 + 2*E*k1*s*t3 + 2*E*t1*t3*s^2 + 2*E*t2*t3*s^2 - k1*k2*s*t1*k3^2 + 2*E*k1*t2*t3*s^2 + 2*E*t1*t2*t3*s^3)

Assemble expression [src]

                          k1                          
------------------------------------------------------
       /                              2              \
       |   1                     k2*k3               |
1 + k1*|-------- - ----------------------------------|
       |1 + s*t1              /     2   2           \|
       \           (1 + s*t2)*\1 + s *t3  + 2*E*s*t3//

$$\frac{k_{1}}{k_{1} \left(- \frac{k_{2} k_{3}^{2}}{\left(s t_{2} + 1\right) \left(s^{2} t_{3}^{2} + 2 e s t_{3} + 1\right)} + \frac{1}{s t_{1} + 1}\right) + 1}$$

k1/(1 + k1*(1/(1 + s*t1) - k2*k3^2/((1 + s*t2)*(1 + s^2*t3^2 + 2*E*s*t3))))

Other calculators

How to use it?

Identical expressions

Similar expressions

Least common denominator k1/(1+k1*(-k2*k3*k3/((t3^2*s^2+2*t3*s*e+1)*(t2*s+1))+1/(t1*s+1)))

The solution

Least common denominator k1/(1+k1(-k2k3k3/((t3^2s^2+2t3se+1)(t2s+1))+1/(t1s+1)))