Mister Exam
How do you w^2/(w-6)-12*w-36/(w-6) in partial fractions?
The solution
You have entered
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2 w 36 ----- - 12*w - ----- w - 6 w - 6
$$\left(\frac{w^{2}}{w - 6} - 12 w\right) - \frac{36}{w - 6}$$
w^2/(w - 6) - 12*w - 36/(w - 6)
Powers
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2
36 w
- ------ - 12*w + ------
-6 + w -6 + w
$$\frac{w^{2}}{w - 6} - 12 w - \frac{36}{w - 6}$$
-36/(-6 + w) - 12*w + w^2/(-6 + w)
Trigonometric part
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2
36 w
- ------ - 12*w + ------
-6 + w -6 + w
$$\frac{w^{2}}{w - 6} - 12 w - \frac{36}{w - 6}$$
-36/(-6 + w) - 12*w + w^2/(-6 + w)
Numerical answer
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-12.0*w - 36.0/(-6.0 + w) + w^2/(-6.0 + w)
-12.0*w - 36.0/(-6.0 + w) + w^2/(-6.0 + w)
Combining rational expressions
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-36 + w*(72 - 11*w)
-------------------
-6 + w
$$\frac{w \left(72 - 11 w\right) - 36}{w - 6}$$
(-36 + w*(72 - 11*w))/(-6 + w)
Assemble expression
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2
36 w
- ------ - 12*w + ------
-6 + w -6 + w
$$\frac{w^{2}}{w - 6} - 12 w - \frac{36}{w - 6}$$
-36/(-6 + w) - 12*w + w^2/(-6 + w)
Rational denominator
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2
-36 + w - 12*w*(-6 + w)
------------------------
-6 + w
$$\frac{w^{2} - 12 w \left(w - 6\right) - 36}{w - 6}$$
(-36 + w^2 - 12*w*(-6 + w))/(-6 + w)