Mister Exam
Least common denominator -x^3/(x-1)^2+3*x^2/(x-1)
The solution
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3 2
-x 3*x
-------- + -----
2 x - 1
(x - 1)
$$\frac{3 x^{2}}{x - 1} + \frac{\left(-1\right) x^{3}}{\left(x - 1\right)^{2}}$$
(-x^3)/(x - 1)^2 + (3*x^2)/(x - 1)
General simplification
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2
x *(-3 + 2*x)
-------------
2
1 + x - 2*x
$$\frac{x^{2} \left(2 x - 3\right)}{x^{2} - 2 x + 1}$$
x^2*(-3 + 2*x)/(1 + x^2 - 2*x)
Fraction decomposition
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1 - 1/(-1 + x)^2 + 2*x
$$2 x + 1 - \frac{1}{\left(x - 1\right)^{2}}$$
1
1 - --------- + 2*x
2
(-1 + x)
Combinatorics
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2
x *(-3 + 2*x)
-------------
2
(-1 + x)
$$\frac{x^{2} \left(2 x - 3\right)}{\left(x - 1\right)^{2}}$$
x^2*(-3 + 2*x)/(-1 + x)^2
Combining rational expressions
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2
x *(-3 + 2*x)
-------------
2
(-1 + x)
$$\frac{x^{2} \left(2 x - 3\right)}{\left(x - 1\right)^{2}}$$
x^2*(-3 + 2*x)/(-1 + x)^2
Assemble expression
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3 2
x 3*x
- --------- + ------
2 -1 + x
(-1 + x)
$$- \frac{x^{3}}{\left(x - 1\right)^{2}} + \frac{3 x^{2}}{x - 1}$$
-x^3/(-1 + x)^2 + 3*x^2/(-1 + x)
Rational denominator
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3 2 2
- x *(-1 + x) + 3*x *(-1 + x)
------------------------------
3
(-1 + x)
$$\frac{- x^{3} \left(x - 1\right) + 3 x^{2} \left(x - 1\right)^{2}}{\left(x - 1\right)^{3}}$$
(-x^3*(-1 + x) + 3*x^2*(-1 + x)^2)/(-1 + x)^3
Common denominator
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1
1 - ------------ + 2*x
2
1 + x - 2*x
$$2 x + 1 - \frac{1}{x^{2} - 2 x + 1}$$
1 - 1/(1 + x^2 - 2*x) + 2*x
Trigonometric part
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3 2
x 3*x
- --------- + ------
2 -1 + x
(-1 + x)
$$- \frac{x^{3}}{\left(x - 1\right)^{2}} + \frac{3 x^{2}}{x - 1}$$
-x^3/(-1 + x)^2 + 3*x^2/(-1 + x)
Numerical answer
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-x^3/(-1.0 + x)^2 + 3.0*x^2/(-1.0 + x)
-x^3/(-1.0 + x)^2 + 3.0*x^2/(-1.0 + x)
Powers
[src]
3 2
x 3*x
- --------- + ------
2 -1 + x
(-1 + x)
$$- \frac{x^{3}}{\left(x - 1\right)^{2}} + \frac{3 x^{2}}{x - 1}$$
-x^3/(-1 + x)^2 + 3*x^2/(-1 + x)