Mister Exam
Expression simplification/
Fraction Decomposition into the simple/
sqrt(1-(1-x*x)*n^0*n^0/(n^1*n^1))
How do you sqrt(1-(1-x*x)*n^0*n^0/(n^1*n^1)) in partial fractions?
The solution
You have entered
[src]
_____________________
/ 0 0
/ (1 - x*x)*n *n
/ 1 - ---------------
/ 1 1
\/ n *n
$$\sqrt{- \frac{n^{0} n^{0} \left(- x x + 1\right)}{n^{1} n^{1}} + 1}$$
sqrt(1 - ((1 - x*x)*n^0)*n^0/(n^1*n^1))
Fraction decomposition
[src]
sqrt(1 - 1/n^2 + x^2/n^2)
$$\sqrt{1 + \frac{x^{2}}{n^{2}} - \frac{1}{n^{2}}}$$
_____________
/ 2
/ 1 x
/ 1 - -- + --
/ 2 2
\/ n n
General simplification
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______________
/ 2 2
/ -1 + n + x
/ ------------
/ 2
\/ n
$$\sqrt{\frac{n^{2} + x^{2} - 1}{n^{2}}}$$
sqrt((-1 + n^2 + x^2)/n^2)
Powers
[src]
_____________
/ 2
/ -1 + x
/ 1 + -------
/ 2
\/ n
$$\sqrt{1 + \frac{x^{2} - 1}{n^{2}}}$$
____________
/ 2
/ 1 - x
/ 1 - ------
/ 2
\/ n
$$\sqrt{1 - \frac{1 - x^{2}}{n^{2}}}$$
sqrt(1 - (1 - x^2)/n^2)
Trigonometric part
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____________
/ 2
/ 1 - x
/ 1 - ------
/ 2
\/ n
$$\sqrt{1 - \frac{1 - x^{2}}{n^{2}}}$$
sqrt(1 - (1 - x^2)/n^2)
Assemble expression
[src]
_____________
/ 2
/ -1 + x
/ 1 + -------
/ 2
\/ n
$$\sqrt{1 + \frac{x^{2} - 1}{n^{2}}}$$
____________
/ 2
/ 1 - x
/ 1 - ------
/ 2
\/ n
$$\sqrt{1 - \frac{1 - x^{2}}{n^{2}}}$$
sqrt(1 - (1 - x^2)/n^2)
Rational denominator
[src]
______________
/ 2 2
/ -1 + n + x
/ ------------
/ 2
\/ n
$$\sqrt{\frac{n^{2} + x^{2} - 1}{n^{2}}}$$
sqrt((-1 + n^2 + x^2)/n^2)
Combinatorics
[src]
_____________
/ 2
/ 1 x
/ 1 - -- + --
/ 2 2
\/ n n
$$\sqrt{1 + \frac{x^{2}}{n^{2}} - \frac{1}{n^{2}}}$$
sqrt(1 - 1/n^2 + x^2/n^2)
Common denominator
[src]
_____________
/ 2
/ 1 x
/ 1 - -- + --
/ 2 2
\/ n n
$$\sqrt{1 + \frac{x^{2}}{n^{2}} - \frac{1}{n^{2}}}$$
sqrt(1 - 1/n^2 + x^2/n^2)
Combining rational expressions
[src]
______________
/ 2 2
/ -1 + n + x
/ ------------
/ 2
\/ n
$$\sqrt{\frac{n^{2} + x^{2} - 1}{n^{2}}}$$
sqrt((-1 + n^2 + x^2)/n^2)