Mister Exam
Expression simplification/
Least common denominator/
((x^3+6*x^2+11*x+6)/(-6))+((-x^3-9*x^2-26*x-24)/6)
Least common denominator ((x^3+6*x^2+11*x+6)/(-6))+((-x^3-9*x^2-26*x-24)/6)
The solution
You have entered
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3 2 3 2
x + 6*x + 11*x + 6 - x - 9*x - 26*x - 24
-------------------- + -----------------------
-6 6
$$\frac{\left(- 26 x + \left(- x^{3} - 9 x^{2}\right)\right) - 24}{6} + \frac{\left(11 x + \left(x^{3} + 6 x^{2}\right)\right) + 6}{-6}$$
(x^3 + 6*x^2 + 11*x + 6)/(-6) + (-x^3 - 9*x^2 - 26*x - 24)/6
Factorization
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(x + 3)*(x + 5/2)*(x + 2)
$$\left(x + \frac{5}{2}\right) \left(x + 3\right) \left(x + 2\right)$$
((x + 3)*(x + 5/2))*(x + 2)
General simplification
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2 3
37*x 5*x x
-5 - ---- - ---- - --
6 2 3
$$- \frac{x^{3}}{3} - \frac{5 x^{2}}{2} - \frac{37 x}{6} - 5$$
-5 - 37*x/6 - 5*x^2/2 - x^3/3
Fraction decomposition
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-5 - 37*x/6 - 5*x^2/2 - x^3/3
$$- \frac{x^{3}}{3} - \frac{5 x^{2}}{2} - \frac{37 x}{6} - 5$$
2 3
37*x 5*x x
-5 - ---- - ---- - --
6 2 3
Rational denominator
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2 3
-180 - 222*x - 90*x - 12*x
----------------------------
36
$$\frac{- 12 x^{3} - 90 x^{2} - 222 x - 180}{36}$$
(-180 - 222*x - 90*x^2 - 12*x^3)/36
Common denominator
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2 3
37*x 5*x x
-5 - ---- - ---- - --
6 2 3
$$- \frac{x^{3}}{3} - \frac{5 x^{2}}{2} - \frac{37 x}{6} - 5$$
-5 - 37*x/6 - 5*x^2/2 - x^3/3
Trigonometric part
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2 3
37*x 5*x x
-5 - ---- - ---- - --
6 2 3
$$- \frac{x^{3}}{3} - \frac{5 x^{2}}{2} - \frac{37 x}{6} - 5$$
-5 - 37*x/6 - 5*x^2/2 - x^3/3
Assemble expression
[src]
2 3
37*x 5*x x
-5 - ---- - ---- - --
6 2 3
$$- \frac{x^{3}}{3} - \frac{5 x^{2}}{2} - \frac{37 x}{6} - 5$$
-5 - 37*x/6 - 5*x^2/2 - x^3/3
Numerical answer
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-5.0 - 2.5*x^2 - 6.16666666666667*x - 0.333333333333333*x^3
-5.0 - 2.5*x^2 - 6.16666666666667*x - 0.333333333333333*x^3
Combinatorics
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-(2 + x)*(3 + x)*(5 + 2*x)
---------------------------
6
$$- \frac{\left(x + 2\right) \left(x + 3\right) \left(2 x + 5\right)}{6}$$
-(2 + x)*(3 + x)*(5 + 2*x)/6
Powers
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2 3
37*x 5*x x
-5 - ---- - ---- - --
6 2 3
$$- \frac{x^{3}}{3} - \frac{5 x^{2}}{2} - \frac{37 x}{6} - 5$$
-5 - 37*x/6 - 5*x^2/2 - x^3/3
Combining rational expressions
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-30 + x*(-26 + x*(-9 - x)) - x*(11 + x*(6 + x))
-----------------------------------------------
6
$$\frac{x \left(x \left(- x - 9\right) - 26\right) - x \left(x \left(x + 6\right) + 11\right) - 30}{6}$$
(-30 + x*(-26 + x*(-9 - x)) - x*(11 + x*(6 + x)))/6