Mister Exam
Expression simplification/
Least common denominator/
(m^2+3*m/m^2+3*m+2-m^2-2*m/m^2-2*m-3)/1/m^2-m-6-5/m+1
Least common denominator (m^2+3*m/m^2+3*m+2-m^2-2*m/m^2-2*m-3)/1/m^2-m-6-5/m+1
The solution
You have entered
[src]
/ 2 3*m 2 2*m \
|m + --- + 3*m + 2 - m - --- - 2*m - 3|
| 2 2 |
| m m |
|---------------------------------------|
\ 1 / 5
----------------------------------------- - m - 6 - - + 1
2 m
m
$$\left(\left(\left(- m + \frac{1^{-1} \left(\left(- 2 m + \left(- \frac{2 m}{m^{2}} + \left(- m^{2} + \left(\left(3 m + \left(m^{2} + \frac{3 m}{m^{2}}\right)\right) + 2\right)\right)\right)\right) - 3\right)}{m^{2}}\right) - 6\right) - \frac{5}{m}\right) + 1$$
((m^2 + (3*m)/m^2 + 3*m + 2 - m^2 - 2*m/m^2 - 2*m - 3)/1)/m^2 - m - 6 - 5/m + 1
Fraction decomposition
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-5 + m^(-3) - m - 1/m^2 - 4/m
$$- m - 5 - \frac{4}{m} - \frac{1}{m^{2}} + \frac{1}{m^{3}}$$
1 1 4
-5 + -- - m - -- - -
3 2 m
m m
General simplification
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1 1 4
-5 + -- - m - -- - -
3 2 m
m m
$$- m - 5 - \frac{4}{m} - \frac{1}{m^{2}} + \frac{1}{m^{3}}$$
-5 + m^(-3) - m - 1/m^2 - 4/m
Numerical answer
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-5.0 - m - 5.0/m + (-1.0 + 1.0*m + 1.0/m)/m^2
-5.0 - m - 5.0/m + (-1.0 + 1.0*m + 1.0/m)/m^2
Trigonometric part
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1
-1 + m + -
5 m
-5 - m - - + ----------
m 2
m
$$- m - 5 - \frac{5}{m} + \frac{m - 1 + \frac{1}{m}}{m^{2}}$$
-5 - m - 5/m + (-1 + m + 1/m)/m^2
Powers
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1
-1 + m + -
5 m
-5 - m - - + ----------
m 2
m
$$- m - 5 - \frac{5}{m} + \frac{m - 1 + \frac{1}{m}}{m^{2}}$$
-5 - m - 5/m + (-1 + m + 1/m)/m^2
Combining rational expressions
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4 3 2
1 - m - m - 5*m - 4*m
------------------------
3
m
$$\frac{- m^{4} - 5 m^{3} - 4 m^{2} - m + 1}{m^{3}}$$
(1 - m - m^4 - 5*m^3 - 4*m^2)/m^3
Combinatorics
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/ 4 2 3\
-\-1 + m + m + 4*m + 5*m /
-----------------------------
3
m
$$- \frac{m^{4} + 5 m^{3} + 4 m^{2} + m - 1}{m^{3}}$$
-(-1 + m + m^4 + 4*m^2 + 5*m^3)/m^3
Rational denominator
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5 4 / 3 2 5 4\
m - 5*m + m*\m + m - m - m - 6*m /
---------------------------------------
5
m
$$\frac{m^{5} - 5 m^{4} + m \left(- m^{5} - 6 m^{4} + m^{3} - m^{2} + m\right)}{m^{5}}$$
(m^5 - 5*m^4 + m*(m + m^3 - m^2 - m^5 - 6*m^4))/m^5
Assemble expression
[src]
1
-1 + m + -
5 m
-5 - m - - + ----------
m 2
m
$$- m - 5 - \frac{5}{m} + \frac{m - 1 + \frac{1}{m}}{m^{2}}$$
-5 - m - 5/m + (-1 + m + 1/m)/m^2
Common denominator
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2
-1 + m + 4*m
-5 - m - -------------
3
m
$$- m - 5 - \frac{4 m^{2} + m - 1}{m^{3}}$$
-5 - m - (-1 + m + 4*m^2)/m^3