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How do you in partial fractions?:
(a^7*a)^2/(-a)^15
1/(x^4-1)
y*(y+((1/(x+(x^2+y^2)^(1/2))*(1+(2*x/(2*(x^2+y^2)^(1/2)))))))-(y/(x^2+y^2)^(1/2))
(x^2-6*x+8)/(x-4)
Factor polynomial:
z^3-9*z^2+16*z+26
z^3+8*i
z^3+8/125
z^3-5*z^2+9*z-45
Least common denominator:
(z-2)/(6*z+(z-2)*(z-2))+(6/(z*z*z-8))
((z^2+1)^2/(4*z^2))/(13+12*((z^2+1)/2*z*z))
-(z^2+1)/(z-(-1-sqrt(3)*i)/2)^2+2*z/(z-(-1-sqrt(3)*i)/2)
-z^3-(-1)*z^2*y*(-x)*z/(z^2+x*y)-y^2*x*(-x)*z/((z^2+x*y)*((z^2+x*y)^2))
Factor squared:
-y^4-y^2+2
y^4-9*y^2-10
-y^4-y^2-2
y^4+8*y^2+6
Least common denominator:
y*(y+((1/(x+(x^2+y^2)^(1/2))*(1+(2*x/(2*(x^2+y^2)^(1/2)))))))-(y/(x^2+y^2)^(1/2))
Identical expressions
y*(y+((one /(x+(x^ two +y^ two)^(one / two))*(one +(two *x/(two *(x^ two +y^ two)^(one / two)))))))-(y/(x^ two +y^ two)^(one / two))
y multiply by (y plus ((1 divide by (x plus (x squared plus y squared ) to the power of (1 divide by 2)) multiply by (1 plus (2 multiply by x divide by (2 multiply by (x squared plus y squared ) to the power of (1 divide by 2))))))) minus (y divide by (x squared plus y squared ) to the power of (1 divide by 2))
y multiply by (y plus ((one divide by (x plus (x to the power of two plus y to the power of two) to the power of (one divide by two)) multiply by (one plus (two multiply by x divide by (two multiply by (x to the power of two plus y to the power of two) to the power of (one divide by two))))))) minus (y divide by (x to the power of two plus y to the power of two) to the power of (one divide by two))
y*(y+((1/(x+(x2+y2)(1/2))*(1+(2*x/(2*(x2+y2)(1/2)))))))-(y/(x2+y2)(1/2))
y*y+1/x+x2+y21/2*1+2*x/2*x2+y21/2-y/x2+y21/2
y*(y+((1/(x+(x²+y²)^(1/2))*(1+(2*x/(2*(x²+y²)^(1/2)))))))-(y/(x²+y²)^(1/2))
y*(y+((1/(x+(x to the power of 2+y to the power of 2) to the power of (1/2))*(1+(2*x/(2*(x to the power of 2+y to the power of 2) to the power of (1/2)))))))-(y/(x to the power of 2+y to the power of 2) to the power of (1/2))
y(y+((1/(x+(x^2+y^2)^(1/2))(1+(2x/(2(x^2+y^2)^(1/2)))))))-(y/(x^2+y^2)^(1/2))
y(y+((1/(x+(x2+y2)(1/2))(1+(2x/(2(x2+y2)(1/2)))))))-(y/(x2+y2)(1/2))
yy+1/x+x2+y21/21+2x/2x2+y21/2-y/x2+y21/2
yy+1/x+x^2+y^2^1/21+2x/2x^2+y^2^1/2-y/x^2+y^2^1/2
y*(y+((1 divide by (x+(x^2+y^2)^(1 divide by 2))*(1+(2*x divide by (2*(x^2+y^2)^(1 divide by 2)))))))-(y divide by (x^2+y^2)^(1 divide by 2))
Similar expressions
y*(y+((1/(x+(x^2+y^2)^(1/2))*(1+(2*x/(2*(x^2+y^2)^(1/2)))))))-(y/(x^2-y^2)^(1/2))
y*(y+((1/(x-(x^2+y^2)^(1/2))*(1+(2*x/(2*(x^2+y^2)^(1/2)))))))-(y/(x^2+y^2)^(1/2))
y*(y-((1/(x+(x^2+y^2)^(1/2))*(1+(2*x/(2*(x^2+y^2)^(1/2)))))))-(y/(x^2+y^2)^(1/2))
y*(y+((1/(x+(x^2+y^2)^(1/2))*(1+(2*x/(2*(x^2-y^2)^(1/2)))))))-(y/(x^2+y^2)^(1/2))
y*(y+((1/(x+(x^2+y^2)^(1/2))*(1+(2*x/(2*(x^2+y^2)^(1/2)))))))+(y/(x^2+y^2)^(1/2))
y*(y+((1/(x+(x^2+y^2)^(1/2))*(1-(2*x/(2*(x^2+y^2)^(1/2)))))))-(y/(x^2+y^2)^(1/2))
y*(y+((1/(x+(x^2-y^2)^(1/2))*(1+(2*x/(2*(x^2+y^2)^(1/2)))))))-(y/(x^2+y^2)^(1/2))

Expression simplification/ Fraction Decomposition into the simple/ y*(y+((1/(x+(x^2+y^2)^(1/2))*(1+(2*x/(2*(x^2+y^2)^(1/2)))))))-(y/(x^2+y^2)^(1/2))

How do you y(y+((1/(x+(x^2+y^2)^(1/2))(1+(2x/(2(x^2+y^2)^(1/2)))))))-(y/(x^2+y^2)^(1/2)) in partial fractions?

The solution

You have entered [src]

  /             2*x      \               
  |    1 + --------------|               
  |             _________|               
  |            /  2    2 |               
  |        2*\/  x  + y  |        y      
y*|y + ------------------| - ------------
  |            _________ |      _________
  |           /  2    2  |     /  2    2 
  \     x + \/  x  + y   /   \/  x  + y

$$y \left(y + \frac{\frac{2 x}{2 \sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right) - \frac{y}{\sqrt{x^{2} + y^{2}}}$$

y*(y + (1 + (2*x)/((2*sqrt(x^2 + y^2))))/(x + sqrt(x^2 + y^2))) - y/sqrt(x^2 + y^2)

Fraction decomposition [src]

y^2

$$y^{2}$$

2
y

General simplification [src]

2
y

$$y^{2}$$

y^2

Assemble expression [src]

  /                            x      \
  |                   1 + ------------|
  |                          _________|
  |                         /  2    2 |
  |         1             \/  x  + y  |
y*|y - ------------ + ----------------|
  |       _________          _________|
  |      /  2    2          /  2    2 |
  \    \/  x  + y     x + \/  x  + y  /

$$y \left(y - \frac{1}{\sqrt{x^{2} + y^{2}}} + \frac{\frac{x}{\sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right)$$

  /             x      \               
  |    1 + ------------|               
  |           _________|               
  |          /  2    2 |               
  |        \/  x  + y  |        y      
y*|y + ----------------| - ------------
  |           _________|      _________
  |          /  2    2 |     /  2    2 
  \    x + \/  x  + y  /   \/  x  + y

$$y \left(y + \frac{\frac{x}{\sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right) - \frac{y}{\sqrt{x^{2} + y^{2}}}$$

y*(y + (1 + x/sqrt(x^2 + y^2))/(x + sqrt(x^2 + y^2))) - y/sqrt(x^2 + y^2)

Rational denominator [src]

                                    2
     2  4      4  2      2 / 2    2\ 
- 2*x *y  - 2*x *y  + 2*y *\x  + y / 
-------------------------------------
               2 / 2    2\           
            2*y *\x  + y /

$$\frac{- 2 x^{4} y^{2} - 2 x^{2} y^{4} + 2 y^{2} \left(x^{2} + y^{2}\right)^{2}}{2 y^{2} \left(x^{2} + y^{2}\right)}$$

(-2*x^2*y^4 - 2*x^4*y^2 + 2*y^2*(x^2 + y^2)^2)/(2*y^2*(x^2 + y^2))

Expand expression [src]

  /             x      \               
  |    1 + ------------|               
  |           _________|               
  |          /  2    2 |               
  |        \/  x  + y  |        y      
y*|y + ----------------| - ------------
  |           _________|      _________
  |          /  2    2 |     /  2    2 
  \    x + \/  x  + y  /   \/  x  + y

$$y \left(y + \frac{\frac{x}{\sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right) - \frac{y}{\sqrt{x^{2} + y^{2}}}$$

y*(y + (1 + x/sqrt(x^2 + y^2))/(x + sqrt(x^2 + y^2))) - y/sqrt(x^2 + y^2)

Common denominator [src]

2
y

$$y^{2}$$

y^2

Trigonometric part [src]

  /             x      \               
  |    1 + ------------|               
  |           _________|               
  |          /  2    2 |               
  |        \/  x  + y  |        y      
y*|y + ----------------| - ------------
  |           _________|      _________
  |          /  2    2 |     /  2    2 
  \    x + \/  x  + y  /   \/  x  + y

$$y \left(y + \frac{\frac{x}{\sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right) - \frac{y}{\sqrt{x^{2} + y^{2}}}$$

y*(y + (1 + x/sqrt(x^2 + y^2))/(x + sqrt(x^2 + y^2))) - y/sqrt(x^2 + y^2)

Numerical answer [src]

y*(y + (1.0 + 1.0*x*(x^2 + y^2)^(-0.5))/(x + (x^2 + y^2)^0.5)) - y*(x^2 + y^2)^(-0.5)

y*(y + (1.0 + 1.0*x*(x^2 + y^2)^(-0.5))/(x + (x^2 + y^2)^0.5)) - y*(x^2 + y^2)^(-0.5)

Combining rational expressions [src]

2
y

$$y^{2}$$

y^2

Powers [src]

  /             x      \               
  |    1 + ------------|               
  |           _________|               
  |          /  2    2 |               
  |        \/  x  + y  |        y      
y*|y + ----------------| - ------------
  |           _________|      _________
  |          /  2    2 |     /  2    2 
  \    x + \/  x  + y  /   \/  x  + y

$$y \left(y + \frac{\frac{x}{\sqrt{x^{2} + y^{2}}} + 1}{x + \sqrt{x^{2} + y^{2}}}\right) - \frac{y}{\sqrt{x^{2} + y^{2}}}$$

y*(y + (1 + x/sqrt(x^2 + y^2))/(x + sqrt(x^2 + y^2))) - y/sqrt(x^2 + y^2)

Combinatorics [src]

2
y

$$y^{2}$$

y^2

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Identical expressions

Similar expressions

How do you y*(y+((1/(x+(x^2+y^2)^(1/2))*(1+(2*x/(2*(x^2+y^2)^(1/2)))))))-(y/(x^2+y^2)^(1/2)) in partial fractions?

The solution

How do you y(y+((1/(x+(x^2+y^2)^(1/2))(1+(2x/(2(x^2+y^2)^(1/2)))))))-(y/(x^2+y^2)^(1/2)) in partial fractions?