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Expression simplification/ Least common denominator/ (z/t-t/z)*5*t*z/z-t

Least common denominator (z/t-t/z)*5*t*z/z-t

An expression to simplify:

The solution

You have entered [src] 
/z   t\          
|- - -|*5*t*z    
\t   z/          
------------- - t
      z
$$- t + \frac{z t 5 \left(- \frac{t}{z} + \frac{z}{t}\right)}{z}$$ 
((((z/t - t/z)*5)*t)*z)/z - t
General simplification [src] 
              2
           5*t 
-t + 5*z - ----
            z
$$- \frac{5 t^{2}}{z} - t + 5 z$$ 
-t + 5*z - 5*t^2/z
Powers [src] 
       /  5*t   5*z\
-t + t*|- --- + ---|
       \   z     t /
$$t \left(- \frac{5 t}{z} + \frac{5 z}{t}\right) - t$$ 
-t + t*(-5*t/z + 5*z/t)
Combining rational expressions [src] 
     2      2      
- 5*t  + 5*z  - t*z
-------------------
         z
$$\frac{- 5 t^{2} - t z + 5 z^{2}}{z}$$ 
(-5*t^2 + 5*z^2 - t*z)/z
Combinatorics [src] 
     2      2      
- 5*t  + 5*z  - t*z
-------------------
         z
$$\frac{- 5 t^{2} - t z + 5 z^{2}}{z}$$ 
(-5*t^2 + 5*z^2 - t*z)/z
Assemble expression [src] 
  /     5*t   5*z\
t*|-1 - --- + ---|
  \      z     t /
$$t \left(- \frac{5 t}{z} - 1 + \frac{5 z}{t}\right)$$ 
       /  5*t   5*z\
-t + t*|- --- + ---|
       \   z     t /
$$t \left(- \frac{5 t}{z} + \frac{5 z}{t}\right) - t$$ 
-t + t*(-5*t/z + 5*z/t)
Numerical answer [src] 
-t + t*(5.0*z/t - 5.0*t/z)
-t + t*(5.0*z/t - 5.0*t/z)
Rational denominator [src] 
   2  2       /     2      2\
- t *z  + t*z*\- 5*t  + 5*z /
-----------------------------
                2            
             t*z
$$\frac{- t^{2} z^{2} + t z \left(- 5 t^{2} + 5 z^{2}\right)}{t z^{2}}$$ 
(-t^2*z^2 + t*z*(-5*t^2 + 5*z^2))/(t*z^2)
Common denominator [src] 
              2
           5*t 
-t + 5*z - ----
            z
$$- \frac{5 t^{2}}{z} - t + 5 z$$ 
-t + 5*z - 5*t^2/z
Trigonometric part [src] 
       /  5*t   5*z\
-t + t*|- --- + ---|
       \   z     t /
$$t \left(- \frac{5 t}{z} + \frac{5 z}{t}\right) - t$$ 
-t + t*(-5*t/z + 5*z/t)
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