Mister Exam

# How do you -2*sqrt(3)/(3*sqrt(1-(2*x-1)^2/3)) in partial fractions?

An expression to simplify:

### The solution

You have entered [src]
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-2*\/ 3
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________________
/              2
/      (2*x - 1)
3*  /   1 - ----------
\/            3      
$$\frac{\left(-1\right) 2 \sqrt{3}}{3 \sqrt{- \frac{\left(2 x - 1\right)^{2}}{3} + 1}}$$
(-2*sqrt(3))/((3*sqrt(1 - (2*x - 1)^2/3)))
Fraction decomposition [src]
-sqrt(2)/sqrt(1 - 2*x^2 + 2*x)
$$- \frac{\sqrt{2}}{\sqrt{- 2 x^{2} + 2 x + 1}}$$
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-\/ 2
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/        2
\/  1 - 2*x  + 2*x 
General simplification [src]
        -2
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/               2
\/  3 - (-1 + 2*x)  
$$- \frac{2}{\sqrt{3 - \left(2 x - 1\right)^{2}}}$$
-2/sqrt(3 - (-1 + 2*x)^2)
Assemble expression [src]
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-2*\/ 3
------------------------
_________________
/               2
/      (-1 + 2*x)
3*  /   1 - -----------
\/             3      
$$- \frac{2 \sqrt{3}}{3 \sqrt{1 - \frac{\left(2 x - 1\right)^{2}}{3}}}$$
-2*sqrt(3)/(3*sqrt(1 - (-1 + 2*x)^2/3))
Expand expression [src]
             ___
-2*\/ 3
-----------------------
________________
/              2
/      (2*x - 1)
3*  /   1 - ----------
\/            3      
$$- \frac{2 \sqrt{3}}{3 \sqrt{- \frac{\left(2 x - 1\right)^{2}}{3} + 1}}$$
-2*sqrt(3)/(3*sqrt(1 - (2*x - 1)^2/3))
Rational denominator [src]
        -2
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/        2
\/  2 - 4*x  + 4*x 
$$- \frac{2}{\sqrt{- 4 x^{2} + 4 x + 2}}$$
-2/sqrt(2 - 4*x^2 + 4*x)
Trigonometric part [src]
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-2*\/ 3
------------------------
_________________
/               2
/      (-1 + 2*x)
3*  /   1 - -----------
\/             3      
$$- \frac{2 \sqrt{3}}{3 \sqrt{1 - \frac{\left(2 x - 1\right)^{2}}{3}}}$$
-2*sqrt(3)/(3*sqrt(1 - (-1 + 2*x)^2/3))
Combinatorics [src]
        -2
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________________
/        2
\/  2 - 4*x  + 4*x 
$$- \frac{2}{\sqrt{- 4 x^{2} + 4 x + 2}}$$
-2/sqrt(2 - 4*x^2 + 4*x)
-1.0*(0.75 - (-0.5 + x)^2)^(-0.5)
-1.0*(0.75 - (-0.5 + x)^2)^(-0.5)
Powers [src]
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-2*\/ 3
------------------------
_________________
/               2
/      (-1 + 2*x)
3*  /   1 - -----------
\/             3      
$$- \frac{2 \sqrt{3}}{3 \sqrt{1 - \frac{\left(2 x - 1\right)^{2}}{3}}}$$
-2*sqrt(3)/(3*sqrt(1 - (-1 + 2*x)^2/3))
Combining rational expressions [src]
        -2
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_________________
/               2
\/  3 - (-1 + 2*x)  
$$- \frac{2}{\sqrt{3 - \left(2 x - 1\right)^{2}}}$$
-2/sqrt(3 - (-1 + 2*x)^2)
Common denominator [src]
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-\/ 2
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________________
/        2
\/  1 - 2*x  + 2*x 
$$- \frac{\sqrt{2}}{\sqrt{- 2 x^{2} + 2 x + 1}}$$
-sqrt(2)/sqrt(1 - 2*x^2 + 2*x)