Mister Exam
How do you (x^2-6*x-9)/(x-3) in partial fractions?
The solution
You have entered
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2 x - 6*x - 9 ------------ x - 3
$$\frac{\left(x^{2} - 6 x\right) - 9}{x - 3}$$
(x^2 - 6*x - 9)/(x - 3)
General simplification
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2
-9 + x - 6*x
-------------
-3 + x
$$\frac{x^{2} - 6 x - 9}{x - 3}$$
(-9 + x^2 - 6*x)/(-3 + x)
Fraction decomposition
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-3 + x - 18/(-3 + x)
$$x - 3 - \frac{18}{x - 3}$$
18
-3 + x - ------
-3 + x
Assemble expression
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2
-9 + x - 6*x
-------------
-3 + x
$$\frac{x^{2} - 6 x - 9}{x - 3}$$
(-9 + x^2 - 6*x)/(-3 + x)
Common denominator
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18
-3 + x - ------
-3 + x
$$x - 3 - \frac{18}{x - 3}$$
-3 + x - 18/(-3 + x)
Powers
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2
-9 + x - 6*x
-------------
-3 + x
$$\frac{x^{2} - 6 x - 9}{x - 3}$$
(-9 + x^2 - 6*x)/(-3 + x)
Rational denominator
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2
-9 + x - 6*x
-------------
-3 + x
$$\frac{x^{2} - 6 x - 9}{x - 3}$$
(-9 + x^2 - 6*x)/(-3 + x)
Trigonometric part
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2
-9 + x - 6*x
-------------
-3 + x
$$\frac{x^{2} - 6 x - 9}{x - 3}$$
(-9 + x^2 - 6*x)/(-3 + x)
Combining rational expressions
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-9 + x*(-6 + x)
---------------
-3 + x
$$\frac{x \left(x - 6\right) - 9}{x - 3}$$
(-9 + x*(-6 + x))/(-3 + x)
Combinatorics
[src]
2
-9 + x - 6*x
-------------
-3 + x
$$\frac{x^{2} - 6 x - 9}{x - 3}$$
(-9 + x^2 - 6*x)/(-3 + x)