Mister Exam
Other calculators
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How to use it?
- Factor polynomial:
- x^4-9
- x^8-y^6
- 0.09-a^2
- y^5+y^3+y^2+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))))
- 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)
- Factor squared:
- -a^4-8*a^2-1
- -q^4-4*q^2+5
- -9*p^2-5*p-4
- 8*x^4-14*x^2-3
- 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
- ((-k2/p)*(k3/(t3*p+ one))+k one *p)*((k5*p)/(one +k3*p*(k3/(t3*p+ one))*(k4*(t4*p+1))))
- (( minus k2 divide by p) multiply by (k3 divide by (t3 multiply by p plus 1)) plus k1 multiply by p) multiply by ((k5 multiply by p) divide by (1 plus k3 multiply by p multiply by (k3 divide by (t3 multiply by p plus 1)) multiply by (k4 multiply by (t4 multiply by p plus 1))))
- (( minus k2 divide by p) multiply by (k3 divide by (t3 multiply by p plus one)) plus k one multiply by p) multiply by ((k5 multiply by p) divide by (one plus k3 multiply by p multiply by (k3 divide by (t3 multiply by p plus one)) multiply by (k4 multiply by (t4 multiply by p plus 1))))
- ((-k2/p)(k3/(t3p+1))+k1p)((k5p)/(1+k3p(k3/(t3p+1))(k4(t4p+1))))
- -k2/pk3/t3p+1+k1pk5p/1+k3pk3/t3p+1k4t4p+1
- ((-k2 divide by p)*(k3 divide by (t3*p+1))+k1*p)*((k5*p) divide by (1+k3*p*(k3 divide by (t3*p+1))*(k4*(t4*p+1))))
-
Similar expressions
- ((-k2/p)*(k3/(t3*p+1))-k1*p)*((k5*p)/(1+k3*p*(k3/(t3*p+1))*(k4*(t4*p+1))))
- ((-k2/p)*(k3/(t3*p-1))+k1*p)*((k5*p)/(1+k3*p*(k3/(t3*p+1))*(k4*(t4*p+1))))
- ((-k2/p)*(k3/(t3*p+1))+k1*p)*((k5*p)/(1+k3*p*(k3/(t3*p+1))*k4*(t4*p+1)))
- ((-k2/p)*(k3/(t3*p+1))+k1*p)*((k5*p)/(1+k3*p*(k3/(t3*p+1))*(k4*(t4*p-1))))
- ((-k2/p)*(k3/(t3*p+1))+k1*p)*((k5*p)/(1+k3*p*(k3/(t3*p-1))*(k4*(t4*p+1))))
- ((-k2/p)*(k3/(t3*p+1))+k1*p)*((k5*p)/(1-k3*p*(k3/(t3*p+1))*(k4*(t4*p+1))))
- ((k2/p)*(k3/(t3*p+1))+k1*p)*((k5*p)/(1+k3*p*(k3/(t3*p+1))*(k4*(t4*p+1))))
- (-k2/p*k3/(t3*p+1)+k1*p)*((k5*p)/(1+k3*p*(k3/(t3*p+1))*k4*(t4*p+1)))
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
[src]
/-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
[src]
/ 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
[src]
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
[src]
/ 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
[src]
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
[src]
/ 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))