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Expression simplification/ Least common denominator/ ((z+p)/(2*(z-p)))-((z-p)/(2*(z+p)))-((p)/(z-p))

Least common denominator ((z+p)/(2*(z-p)))-((z-p)/(2*(z+p)))-((p)/(z-p))

An expression to simplify:

The solution

You have entered [src] 
  z + p       z - p       p  
--------- - --------- - -----
2*(z - p)   2*(z + p)   z - p
$$- \frac{p}{- p + z} + \left(- \frac{- p + z}{2 \left(p + z\right)} + \frac{p + z}{2 \left(- p + z\right)}\right)$$ 
(z + p)/((2*(z - p))) - (z - p)/(2*(z + p)) - p/(z - p)
General simplification [src] 
  p  
-----
p + z
$$\frac{p}{p + z}$$ 
p/(p + z)
Powers [src] 
  p + z        p       z - p  
---------- - ----- - ---------
-2*p + 2*z   z - p   2*p + 2*z
$$- \frac{p}{- p + z} - \frac{- p + z}{2 p + 2 z} + \frac{p + z}{- 2 p + 2 z}$$ 
  p + z        p - z       p  
---------- + --------- - -----
-2*p + 2*z   2*p + 2*z   z - p
$$- \frac{p}{- p + z} + \frac{p - z}{2 p + 2 z} + \frac{p + z}{- 2 p + 2 z}$$ 
(p + z)/(-2*p + 2*z) + (p - z)/(2*p + 2*z) - p/(z - p)
Combinatorics [src] 
  p  
-----
p + z
$$\frac{p}{p + z}$$ 
p/(p + z)
Assemble expression [src] 
  p + z        p       z - p  
---------- - ----- - ---------
-2*p + 2*z   z - p   2*p + 2*z
$$- \frac{p}{- p + z} - \frac{- p + z}{2 p + 2 z} + \frac{p + z}{- 2 p + 2 z}$$ 
(p + z)/(-2*p + 2*z) - p/(z - p) - (z - p)/(2*p + 2*z)
Expand expression [src] 
  z + p       p       z - p  
--------- - ----- - ---------
2*(z - p)   z - p   2*(z + p)
$$- \frac{p}{- p + z} - \frac{- p + z}{2 \left(p + z\right)} + \frac{p + z}{2 \left(- p + z\right)}$$ 
(z + p)/(2*(z - p)) - p/(z - p) - (z - p)/(2*(z + p))
Numerical answer [src] 
(p + z)/(2.0*z - 2.0*p) - p/(z - p) - (z - p)/(2.0*p + 2.0*z)
(p + z)/(2.0*z - 2.0*p) - p/(z - p) - (z - p)/(2.0*p + 2.0*z)
Rational denominator [src] 
(z - p)*((p + z)*(2*p + 2*z) + (p - z)*(-2*p + 2*z)) - p*(-2*p + 2*z)*(2*p + 2*z)
---------------------------------------------------------------------------------
                         (z - p)*(-2*p + 2*z)*(2*p + 2*z)
$$\frac{- p \left(- 2 p + 2 z\right) \left(2 p + 2 z\right) + \left(- p + z\right) \left(\left(- 2 p + 2 z\right) \left(p - z\right) + \left(p + z\right) \left(2 p + 2 z\right)\right)}{\left(- 2 p + 2 z\right) \left(- p + z\right) \left(2 p + 2 z\right)}$$ 
((z - p)*((p + z)*(2*p + 2*z) + (p - z)*(-2*p + 2*z)) - p*(-2*p + 2*z)*(2*p + 2*z))/((z - p)*(-2*p + 2*z)*(2*p + 2*z))
Common denominator [src] 
  p  
-----
p + z
$$\frac{p}{p + z}$$ 
p/(p + z)
Combining rational expressions [src] 
       2          2              
(p + z)  - (z - p)  - 2*p*(p + z)
---------------------------------
        2*(p + z)*(z - p)
$$\frac{- 2 p \left(p + z\right) - \left(- p + z\right)^{2} + \left(p + z\right)^{2}}{2 \left(- p + z\right) \left(p + z\right)}$$ 
((p + z)^2 - (z - p)^2 - 2*p*(p + z))/(2*(p + z)*(z - p))
Trigonometric part [src] 
  p + z        p       z - p  
---------- - ----- - ---------
-2*p + 2*z   z - p   2*p + 2*z
$$- \frac{p}{- p + z} - \frac{- p + z}{2 p + 2 z} + \frac{p + z}{- 2 p + 2 z}$$ 
(p + z)/(-2*p + 2*z) - p/(z - p) - (z - p)/(2*p + 2*z)
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