Mister Exam
Least common denominator y/(y+3)^2-y/(y^2)-9
The solution
You have entered
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y y
-------- - -- - 9
2 2
(y + 3) y
$$\left(\frac{y}{\left(y + 3\right)^{2}} - \frac{y}{y^{2}}\right) - 9$$
y/(y + 3)^2 - y/y^2 - 9
Fraction decomposition
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-9 + 1/(3 + y) - 1/y - 3/(3 + y)^2
$$-9 + \frac{1}{y + 3} - \frac{3}{\left(y + 3\right)^{2}} - \frac{1}{y}$$
1 1 3
-9 + ----- - - - --------
3 + y y 2
(3 + y)
General simplification
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1 y
-9 - - + --------
y 2
(3 + y)
$$\frac{y}{\left(y + 3\right)^{2}} - 9 - \frac{1}{y}$$
-9 - 1/y + y/(3 + y)^2
Rational denominator
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3 2 2 2
y - y*(3 + y) - 9*y *(3 + y)
-------------------------------
2 2
y *(3 + y)
$$\frac{y^{3} - 9 y^{2} \left(y + 3\right)^{2} - y \left(y + 3\right)^{2}}{y^{2} \left(y + 3\right)^{2}}$$
(y^3 - y*(3 + y)^2 - 9*y^2*(3 + y)^2)/(y^2*(3 + y)^2)
Powers
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1 y
-9 - - + --------
y 2
(3 + y)
$$\frac{y}{\left(y + 3\right)^{2}} - 9 - \frac{1}{y}$$
-9 - 1/y + y/(3 + y)^2
Numerical answer
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-9.0 - 1/y + 0.111111111111111*y/(1 + 0.333333333333333*y)^2
-9.0 - 1/y + 0.111111111111111*y/(1 + 0.333333333333333*y)^2
Common denominator
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9 + 6*y
-9 - ---------------
3 2
y + 6*y + 9*y
$$- \frac{6 y + 9}{y^{3} + 6 y^{2} + 9 y} - 9$$
-9 - (9 + 6*y)/(y^3 + 6*y^2 + 9*y)
Combining rational expressions
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2 2 2
y - (3 + y) - 9*y*(3 + y)
----------------------------
2
y*(3 + y)
$$\frac{y^{2} - 9 y \left(y + 3\right)^{2} - \left(y + 3\right)^{2}}{y \left(y + 3\right)^{2}}$$
(y^2 - (3 + y)^2 - 9*y*(3 + y)^2)/(y*(3 + y)^2)
Combinatorics
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/ 3 2 \
-3*\3 + 3*y + 18*y + 29*y/
----------------------------
2
y*(3 + y)
$$- \frac{3 \left(3 y^{3} + 18 y^{2} + 29 y + 3\right)}{y \left(y + 3\right)^{2}}$$
-3*(3 + 3*y^3 + 18*y^2 + 29*y)/(y*(3 + y)^2)
Assemble expression
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1 y
-9 - - + --------
y 2
(3 + y)
$$\frac{y}{\left(y + 3\right)^{2}} - 9 - \frac{1}{y}$$
-9 - 1/y + y/(3 + y)^2
Trigonometric part
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1 y
-9 - - + --------
y 2
(3 + y)
$$\frac{y}{\left(y + 3\right)^{2}} - 9 - \frac{1}{y}$$
-9 - 1/y + y/(3 + y)^2