Mister Exam
Expression simplification/
Fraction Decomposition into the simple/
(z/(z-1))+((z^2-1.0923*z)/(z^2-1.9061*z+0.9277))
How do you (z/(z-1))+((z^2-1.0923*z)/(z^2-1.9061*z+0.9277)) in partial fractions?
The solution
You have entered
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2
z z - 1.0923*z
----- + ----------------------
z - 1 2
z - 1.9061*z + 0.9277
$$\frac{z}{z - 1} + \frac{z^{2} - 1.0923 z}{\left(z^{2} - 1.9061 z\right) + 0.9277}$$
z/(z - 1) + (z^2 - 1.0923*z)/(z^2 - 1.9061*z + 0.9277)
Fraction decomposition
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2.0 + 1.25515295413097*(0.508663230617392 + 0.49725847132361*z^2 - 1.0*z)/(-0.31922507828361 + 0.344103781700561*z^3 + 0.975121296583049*z - 1.0*z^2)
$$\frac{1.25515295413097 \left(0.49725847132361 z^{2} - 1.0 z + 0.508663230617392\right)}{0.344103781700561 z^{3} - 1.0 z^{2} + 0.975121296583049 z - 0.31922507828361} + 2.0$$
/ 2 \
1.25515295413097*\0.508663230617392 + 0.49725847132361*z - 1.0*z/
2.0 + -----------------------------------------------------------------------
3 2
-0.31922507828361 + 0.344103781700561*z + 0.975121296583049*z - 1.0*z
General simplification
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/ 2 \
z*\0.9277 + z - 1.9061*z + (-1 + z)*(-1.0923 + z)/
---------------------------------------------------
/ 2 \
(-1 + z)*\0.9277 + z - 1.9061*z/
$$\frac{z \left(z^{2} - 1.9061 z + \left(z - 1.0923\right) \left(z - 1\right) + 0.9277\right)}{\left(z - 1\right) \left(z^{2} - 1.9061 z + 0.9277\right)}$$
z*(0.9277 + z^2 - 1.9061*z + (-1 + z)*(-1.0923 + z))/((-1 + z)*(0.9277 + z^2 - 1.9061*z))
Rational denominator
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/ 2 \ / 2 \
z*\0.9277 + z - 1.9061*z/ + (-1 + z)*\z - 1.0923*z/
-----------------------------------------------------
/ 2 \
(-1 + z)*\0.9277 + z - 1.9061*z/
$$\frac{z \left(z^{2} - 1.9061 z + 0.9277\right) + \left(z - 1\right) \left(z^{2} - 1.0923 z\right)}{\left(z - 1\right) \left(z^{2} - 1.9061 z + 0.9277\right)}$$
(z*(0.9277 + z^2 - 1.9061*z) + (-1 + z)*(z^2 - 1.0923*z))/((-1 + z)*(0.9277 + z^2 - 1.9061*z))
Assemble expression
[src]
2
z z - 1.0923*z
------ + ----------------------
-1 + z 2
0.9277 + z - 1.9061*z
$$\frac{z}{z - 1} + \frac{z^{2} - 1.0923 z}{z^{2} - 1.9061 z + 0.9277}$$
z/(-1 + z) + (z^2 - 1.0923*z)/(0.9277 + z^2 - 1.9061*z)
Common denominator
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/ 2 \
1.0*\1.8554 + 1.8138*z - 3.6476*z/
2.0 + ---------------------------------------
3 2
-0.9277 + 1.0*z + 2.8338*z - 2.9061*z
$$\frac{1.0 \left(1.8138 z^{2} - 3.6476 z + 1.8554\right)}{1.0 z^{3} - 2.9061 z^{2} + 2.8338 z - 0.9277} + 2.0$$
2.0 + 1.0*(1.8554 + 1.8138*z^2 - 3.6476*z)/(-0.9277 + 1.0*z^3 + 2.8338*z - 2.9061*z^2)
Trigonometric part
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2
z z - 1.0923*z
------ + ----------------------
-1 + z 2
0.9277 + z - 1.9061*z
$$\frac{z}{z - 1} + \frac{z^{2} - 1.0923 z}{z^{2} - 1.9061 z + 0.9277}$$
z/(-1 + z) + (z^2 - 1.0923*z)/(0.9277 + z^2 - 1.9061*z)
Combining rational expressions
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z*(0.9277 + z*(-1.9061 + z) + (-1 + z)*(-1.0923 + z))
-----------------------------------------------------
(-1 + z)*(0.9277 + z*(-1.9061 + z))
$$\frac{z \left(z \left(z - 1.9061\right) + \left(z - 1.0923\right) \left(z - 1\right) + 0.9277\right)}{\left(z - 1\right) \left(z \left(z - 1.9061\right) + 0.9277\right)}$$
z*(0.9277 + z*(-1.9061 + z) + (-1 + z)*(-1.0923 + z))/((-1 + z)*(0.9277 + z*(-1.9061 + z)))
Combinatorics
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/ 2 \
2.09768637532134*z*\0.505202080832333 + 0.500200080032013*z - 1.0*z/
---------------------------------------------------------------------
/ 2 \
(-1 + z)*\0.486700592833534 + 0.524631446408898*z - 1.0*z/
$$\frac{2.09768637532134 z \left(0.500200080032013 z^{2} - 1.0 z + 0.505202080832333\right)}{\left(z - 1\right) \left(0.524631446408898 z^{2} - 1.0 z + 0.486700592833534\right)}$$
2.09768637532134*z*(0.505202080832333 + 0.500200080032013*z^2 - 1.0*z)/((-1 + z)*(0.486700592833534 + 0.524631446408898*z^2 - 1.0*z))
Powers
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2
z z - 1.0923*z
------ + ----------------------
-1 + z 2
0.9277 + z - 1.9061*z
$$\frac{z}{z - 1} + \frac{z^{2} - 1.0923 z}{z^{2} - 1.9061 z + 0.9277}$$
z/(-1 + z) + (z^2 - 1.0923*z)/(0.9277 + z^2 - 1.9061*z)
Numerical answer
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z/(-1.0 + z) + (z^2 - 1.0923*z)/(0.9277 + z^2 - 1.9061*z)
z/(-1.0 + z) + (z^2 - 1.0923*z)/(0.9277 + z^2 - 1.9061*z)