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Expression simplification/ Least common denominator/ tan(x)+tan(y)/tan(x+y)+tan(x)-tan(y)/tan(x-y)

Least common denominator tan(x)+tan(y)/tan(x+y)+tan(x)-tan(y)/tan(x-y)

An expression to simplify:

The solution

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           tan(y)                tan(y)  
tan(x) + ---------- + tan(x) - ----------
         tan(x + y)            tan(x - y)
$$\left(\left(\tan{\left(x \right)} + \frac{\tan{\left(y \right)}}{\tan{\left(x + y \right)}}\right) + \tan{\left(x \right)}\right) - \frac{\tan{\left(y \right)}}{\tan{\left(x - y \right)}}$$ 
tan(x) + tan(y)/tan(x + y) + tan(x) - tan(y)/tan(x - y)
General simplification [src] 
             tan(y)       tan(y)  
2*tan(x) + ---------- - ----------
           tan(x + y)   tan(x - y)
$$2 \tan{\left(x \right)} + \frac{\tan{\left(y \right)}}{\tan{\left(x + y \right)}} - \frac{\tan{\left(y \right)}}{\tan{\left(x - y \right)}}$$ 
2*tan(x) + tan(y)/tan(x + y) - tan(y)/tan(x - y)
Common denominator [src] 
           tan(y)*tan(x + y) - tan(y)*tan(x - y)
2*tan(x) - -------------------------------------
                   tan(x + y)*tan(x - y)
$$- \frac{- \tan{\left(y \right)} \tan{\left(x - y \right)} + \tan{\left(y \right)} \tan{\left(x + y \right)}}{\tan{\left(x - y \right)} \tan{\left(x + y \right)}} + 2 \tan{\left(x \right)}$$ 
2*tan(x) - (tan(y)*tan(x + y) - tan(y)*tan(x - y))/(tan(x + y)*tan(x - y))
Numerical answer [src] 
2*tan(x) + tan(y)/tan(x + y) - tan(y)/tan(x - y)
2*tan(x) + tan(y)/tan(x + y) - tan(y)/tan(x - y)
Combining rational expressions [src] 
(2*tan(x)*tan(x + y) + tan(y))*tan(x - y) - tan(y)*tan(x + y)
-------------------------------------------------------------
                    tan(x + y)*tan(x - y)
$$\frac{\left(2 \tan{\left(x \right)} \tan{\left(x + y \right)} + \tan{\left(y \right)}\right) \tan{\left(x - y \right)} - \tan{\left(y \right)} \tan{\left(x + y \right)}}{\tan{\left(x - y \right)} \tan{\left(x + y \right)}}$$ 
((2*tan(x)*tan(x + y) + tan(y))*tan(x - y) - tan(y)*tan(x + y))/(tan(x + y)*tan(x - y))
Rational denominator [src] 
(2*tan(x)*tan(x + y) + tan(y))*tan(x - y) - tan(y)*tan(x + y)
-------------------------------------------------------------
                    tan(x + y)*tan(x - y)
$$\frac{\left(2 \tan{\left(x \right)} \tan{\left(x + y \right)} + \tan{\left(y \right)}\right) \tan{\left(x - y \right)} - \tan{\left(y \right)} \tan{\left(x + y \right)}}{\tan{\left(x - y \right)} \tan{\left(x + y \right)}}$$ 
((2*tan(x)*tan(x + y) + tan(y))*tan(x - y) - tan(y)*tan(x + y))/(tan(x + y)*tan(x - y))
Powers [src] 
    /   I*x    -I*x\   /   I*y    -I*y\ / I*(x + y)    I*(-x - y)\   /   I*y    -I*y\ / I*(x - y)    I*(y - x)\
2*I*\- e    + e    /   \- e    + e    /*\e          + e          /   \- e    + e    /*\e          + e         /
-------------------- + ------------------------------------------- - ------------------------------------------
     I*x    -I*x       /   I*(x + y)    I*(-x - y)\ / I*y    -I*y\   /   I*(x - y)    I*(y - x)\ / I*y    -I*y\
    e    + e           \- e          + e          /*\e    + e    /   \- e          + e         /*\e    + e    /
$$\frac{2 i \left(- e^{i x} + e^{- i x}\right)}{e^{i x} + e^{- i x}} - \frac{\left(- e^{i y} + e^{- i y}\right) \left(e^{i \left(- x + y\right)} + e^{i \left(x - y\right)}\right)}{\left(e^{i y} + e^{- i y}\right) \left(e^{i \left(- x + y\right)} - e^{i \left(x - y\right)}\right)} + \frac{\left(- e^{i y} + e^{- i y}\right) \left(e^{i \left(- x - y\right)} + e^{i \left(x + y\right)}\right)}{\left(e^{i y} + e^{- i y}\right) \left(e^{i \left(- x - y\right)} - e^{i \left(x + y\right)}\right)}$$ 
             tan(y)       tan(y)  
2*tan(x) + ---------- - ----------
           tan(x + y)   tan(x - y)
$$2 \tan{\left(x \right)} + \frac{\tan{\left(y \right)}}{\tan{\left(x + y \right)}} - \frac{\tan{\left(y \right)}}{\tan{\left(x - y \right)}}$$ 
2*tan(x) + tan(y)/tan(x + y) - tan(y)/tan(x - y)
Combinatorics [src] 
tan(y)*tan(x - y) - tan(y)*tan(x + y) + 2*tan(x)*tan(x + y)*tan(x - y)
----------------------------------------------------------------------
                        tan(x + y)*tan(x - y)
$$\frac{2 \tan{\left(x \right)} \tan{\left(x - y \right)} \tan{\left(x + y \right)} + \tan{\left(y \right)} \tan{\left(x - y \right)} - \tan{\left(y \right)} \tan{\left(x + y \right)}}{\tan{\left(x - y \right)} \tan{\left(x + y \right)}}$$ 
(tan(y)*tan(x - y) - tan(y)*tan(x + y) + 2*tan(x)*tan(x + y)*tan(x - y))/(tan(x + y)*tan(x - y))
Expand expression [src] 
                                                    2                  2          
                tan(y)            tan(y)         tan (y)*tan(x)     tan (y)*tan(x)
2*tan(x) + --------------- - ---------------- - ---------------- - ---------------
           tan(x) + tan(y)   -tan(y) + tan(x)   -tan(y) + tan(x)   tan(x) + tan(y)
$$2 \tan{\left(x \right)} - \frac{\tan{\left(x \right)} \tan^{2}{\left(y \right)}}{\tan{\left(x \right)} + \tan{\left(y \right)}} + \frac{\tan{\left(y \right)}}{\tan{\left(x \right)} + \tan{\left(y \right)}} - \frac{\tan{\left(x \right)} \tan^{2}{\left(y \right)}}{\tan{\left(x \right)} - \tan{\left(y \right)}} - \frac{\tan{\left(y \right)}}{\tan{\left(x \right)} - \tan{\left(y \right)}}$$ 
2*tan(x) + tan(y)/(tan(x) + tan(y)) - tan(y)/(-tan(y) + tan(x)) - tan(y)^2*tan(x)/(-tan(y) + tan(x)) - tan(y)^2*tan(x)/(tan(x) + tan(y))
Assemble expression [src] 
             tan(y)       tan(y)  
2*tan(x) + ---------- - ----------
           tan(x + y)   tan(x - y)
$$2 \tan{\left(x \right)} + \frac{\tan{\left(y \right)}}{\tan{\left(x + y \right)}} - \frac{\tan{\left(y \right)}}{\tan{\left(x - y \right)}}$$ 
2*tan(x) + tan(y)/tan(x + y) - tan(y)/tan(x - y)
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