Mister Exam
Other calculators
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How to use it?
- Factor polynomial:
- a*m^2+b*m^2-c*n-b*n+c*m^2-a*n
- x^3+64
- x1*x2+x1^2*x3^2+x2*x3
- 49-m^2
- Least common denominator:
- (z^5-5*z^3+10*z-1/10*z+1/5*z^3-1/z^5)*(z^3-3*z+1/3*z-1/z^3)
- ((x^3+y^3)/(x+y))/(x^2-y^2)+(2*y)/(x+y)-(x*y)/(x^2-y^2)
- (y/x-y+x/x+y)/(1/x2/y2)
- ((x*x^(1/2)-x)^3)/(((x^(3/4)-1)/(x^(1/4)-1)-x^(1/2))*(1-x))^3
- Factor squared:
- 2*p^4+p^2-2
- -y^4-14*y^2-2
- x^2-9*x-5
- 2*p^2+3*p-2
- How do you in partial fractions?:
- ((p+3)/(p^2-2p))*((4p-8)/(p+3))
- (a^-2-a/a^-1-1)/(a^2+1)
- 6/(c-1)-10/(((c-1)^2)*10*(c^2))-1-2*c+2/c-1
- (t^4+9)/(t^4+9t^2)
- Least common denominator:
- (a^-2-a/a^-1-1)/(a^2+1)
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Identical expressions
- (a^- two -a/a^- one - one)/(a^ two + one)
- (a to the power of minus 2 minus a divide by a to the power of minus 1 minus 1) divide by (a squared plus 1)
- (a to the power of minus two minus a divide by a to the power of minus one minus one) divide by (a to the power of two plus one)
- (a-2-a/a-1-1)/(a2+1)
- a-2-a/a-1-1/a2+1
- (a^-2-a/a^-1-1)/(a²+1)
- (a to the power of -2-a/a to the power of -1-1)/(a to the power of 2+1)
- a^-2-a/a^-1-1/a^2+1
- (a^-2-a divide by a^-1-1) divide by (a^2+1)
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Similar expressions
- (a^-2-a/a^-1-1)/(a^2-1)
- (a^-2-a/a^-1+1)/(a^2+1)
- (a^+2-a/a^-1-1)/(a^2+1)
- (a^-2-a/a^+1-1)/(a^2+1)
- (a^-2+a/a^-1-1)/(a^2+1)
How do you (a^-2-a/a^-1-1)/(a^2+1) in partial fractions?
The solution
You have entered
[src]
1 a
-- - --- - 1
2 /1\
a |-|
\a/
------------
2
a + 1
$$\frac{\left(\frac{1}{a^{2}} - \frac{a}{\frac{1}{a}}\right) - 1}{a^{2} + 1}$$
(a^(-2) - a/1/a - 1)/(a^2 + 1)
Fraction decomposition
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-1 + a^(-2) - 1/(1 + a^2)
$$-1 - \frac{1}{a^{2} + 1} + \frac{1}{a^{2}}$$
1 1
-1 + -- - ------
2 2
a 1 + a
General simplification
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2 4 1 - a - a ----------- 2 / 2\ a *\1 + a /
$$\frac{- a^{4} - a^{2} + 1}{a^{2} \left(a^{2} + 1\right)}$$
(1 - a^2 - a^4)/(a^2*(1 + a^2))
Rational denominator
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2 4 1 - a - a ----------- 2 / 2\ a *\1 + a /
$$\frac{- a^{4} - a^{2} + 1}{a^{2} \left(a^{2} + 1\right)}$$
(1 - a^2 - a^4)/(a^2*(1 + a^2))
Combining rational expressions
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2 4 1 - a - a ----------- 2 / 2\ a *\1 + a /
$$\frac{- a^{4} - a^{2} + 1}{a^{2} \left(a^{2} + 1\right)}$$
(1 - a^2 - a^4)/(a^2*(1 + a^2))
Combinatorics
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/ 2 4\ -\-1 + a + a / ---------------- 2 / 2\ a *\1 + a /
$$- \frac{a^{4} + a^{2} - 1}{a^{2} \left(a^{2} + 1\right)}$$
-(-1 + a^2 + a^4)/(a^2*(1 + a^2))
Powers
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1 2
-1 + -- - a
2
a
------------
2
1 + a
$$\frac{- a^{2} - 1 + \frac{1}{a^{2}}}{a^{2} + 1}$$
(-1 + a^(-2) - a^2)/(1 + a^2)
Common denominator
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1
-1 + -------
2 4
a + a
$$-1 + \frac{1}{a^{4} + a^{2}}$$
-1 + 1/(a^2 + a^4)
Trigonometric part
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1 2
-1 + -- - a
2
a
------------
2
1 + a
$$\frac{- a^{2} - 1 + \frac{1}{a^{2}}}{a^{2} + 1}$$
(-1 + a^(-2) - a^2)/(1 + a^2)
Assemble expression
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1 2
-1 + -- - a
2
a
------------
2
1 + a
$$\frac{- a^{2} - 1 + \frac{1}{a^{2}}}{a^{2} + 1}$$
(-1 + a^(-2) - a^2)/(1 + a^2)