Mister Exam
Least common denominator (x/sqrt(x^2-y^2))^2+(-y/sqrt(x^2-y^2))^2
The solution
You have entered
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2 2 / x \ / -y \ |------------| + |------------| | _________| | _________| | / 2 2 | | / 2 2 | \\/ x - y / \\/ x - y /
$$\left(\frac{x}{\sqrt{x^{2} - y^{2}}}\right)^{2} + \left(\frac{\left(-1\right) y}{\sqrt{x^{2} - y^{2}}}\right)^{2}$$
(x/sqrt(x^2 - y^2))^2 + ((-y)/sqrt(x^2 - y^2))^2
General simplification
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2 2 x + y ------- 2 2 x - y
$$\frac{x^{2} + y^{2}}{x^{2} - y^{2}}$$
(x^2 + y^2)/(x^2 - y^2)
Combining rational expressions
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2 2 x + y ------- 2 2 x - y
$$\frac{x^{2} + y^{2}}{x^{2} - y^{2}}$$
(x^2 + y^2)/(x^2 - y^2)
Common denominator
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2
2*y
1 + -------
2 2
x - y
$$\frac{2 y^{2}}{x^{2} - y^{2}} + 1$$
1 + 2*y^2/(x^2 - y^2)
Trigonometric part
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2 2 x y ------- + ------- 2 2 2 2 x - y x - y
$$\frac{x^{2}}{x^{2} - y^{2}} + \frac{y^{2}}{x^{2} - y^{2}}$$
x^2/(x^2 - y^2) + y^2/(x^2 - y^2)
Powers
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2 2 x y ------- + ------- 2 2 2 2 x - y x - y
$$\frac{x^{2}}{x^{2} - y^{2}} + \frac{y^{2}}{x^{2} - y^{2}}$$
x^2/(x^2 - y^2) + y^2/(x^2 - y^2)
Rational denominator
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2 2 x + y ------- 2 2 x - y
$$\frac{x^{2} + y^{2}}{x^{2} - y^{2}}$$
(x^2 + y^2)/(x^2 - y^2)
Assemble expression
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2 2 x y ------- + ------- 2 2 2 2 x - y x - y
$$\frac{x^{2}}{x^{2} - y^{2}} + \frac{y^{2}}{x^{2} - y^{2}}$$
x^2/(x^2 - y^2) + y^2/(x^2 - y^2)
Numerical answer
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x^2*(x^2 - y^2)^(-1.0) + y^2*(x^2 - y^2)^(-1.0)
x^2*(x^2 - y^2)^(-1.0) + y^2*(x^2 - y^2)^(-1.0)
Combinatorics
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2 2
x + y
---------------
(x + y)*(x - y)
$$\frac{x^{2} + y^{2}}{\left(x - y\right) \left(x + y\right)}$$
(x^2 + y^2)/((x + y)*(x - y))