Mister Exam
Other calculators
-
How to use it?
- Factor polynomial:
- y^5+y^3+y^2+1
- a^2+8*a+16
- x^4-81
- y^2-81
- 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)))
- factorial(n)/factorial(n+1)-(n-1)/factorial(n)
- (x1/3-y1/3)/(x+y)+1/(x2/3-x1/3*y1/3+y2/3)
- 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
- Factor squared:
- -q^4-4*q^2+5
- -9*p^2-5*p-4
- 8*x^4-14*x^2-3
- x^2-x*a+4*a^2
- How do you in partial fractions?:
- (6x^2+29x)/(x+5)
- 3*x^2/(8-x^4)+4*x^6/(8-x^4)^2
- (x^3+12*x)*(x/(2*(x^3+12*x))+(-12-3*x^2)*(x^2+4)/(4*(x^3+12*x)^2))/(x^2+4)
- 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*(-k2*k3*k3/((t3^2*s^2+2*t3*s*e+1)*(t2*s+1))+1/(t1*s+1)))
The solution
You have entered
[src]
k1
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/ -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))))
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
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k1*(1 + s*t1)*(1 + s*t2)*(1 + s*t3*(2*E + s*t3)) ----------------------------------------------------------------------------------------------------------- / 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/
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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 /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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))))