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Least common denominator exp(x)/x^7-7*exp(x)/x^8

An expression to simplify:

The solution

You have entered [src]
 x      x
e    7*e 
-- - ----
 7     8 
x     x  
$$- \frac{7 e^{x}}{x^{8}} + \frac{e^{x}}{x^{7}}$$
exp(x)/x^7 - 7*exp(x)/x^8
General simplification [src]
          x
(-7 + x)*e 
-----------
      8    
     x     
$$\frac{\left(x - 7\right) e^{x}}{x^{8}}$$
(-7 + x)*exp(x)/x^8
Common denominator [src]
     x      x
- 7*e  + x*e 
-------------
       8     
      x      
$$\frac{x e^{x} - 7 e^{x}}{x^{8}}$$
(-7*exp(x) + x*exp(x))/x^8
Numerical answer [src]
exp(x)/x^7 - 7.0*exp(x)/x^8
exp(x)/x^7 - 7.0*exp(x)/x^8
Rational denominator [src]
 8  x      7  x
x *e  - 7*x *e 
---------------
       15      
      x        
$$\frac{x^{8} e^{x} - 7 x^{7} e^{x}}{x^{15}}$$
(x^8*exp(x) - 7*x^7*exp(x))/x^15
Combinatorics [src]
          x
(-7 + x)*e 
-----------
      8    
     x     
$$\frac{\left(x - 7\right) e^{x}}{x^{8}}$$
(-7 + x)*exp(x)/x^8
Combining rational expressions [src]
          x
(-7 + x)*e 
-----------
      8    
     x     
$$\frac{\left(x - 7\right) e^{x}}{x^{8}}$$
(-7 + x)*exp(x)/x^8
Powers [src]
 x      x
e    7*e 
-- - ----
 7     8 
x     x  
$$\frac{e^{x}}{x^{7}} - \frac{7 e^{x}}{x^{8}}$$
exp(x)/x^7 - 7*exp(x)/x^8
Assemble expression [src]
 x      x
e    7*e 
-- - ----
 7     8 
x     x  
$$\frac{e^{x}}{x^{7}} - \frac{7 e^{x}}{x^{8}}$$
exp(x)/x^7 - 7*exp(x)/x^8
Trigonometric part [src]
cosh(x) + sinh(x)   7*(cosh(x) + sinh(x))
----------------- - ---------------------
         7                     8         
        x                     x          
$$\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{x^{7}} - \frac{7 \left(\sinh{\left(x \right)} + \cosh{\left(x \right)}\right)}{x^{8}}$$
 x      x
e    7*e 
-- - ----
 7     8 
x     x  
$$\frac{e^{x}}{x^{7}} - \frac{7 e^{x}}{x^{8}}$$
cosh(x) + sinh(x)   7*cosh(x) + 7*sinh(x)
----------------- - ---------------------
         7                     8         
        x                     x          
$$\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)}}{x^{7}} - \frac{7 \sinh{\left(x \right)} + 7 \cosh{\left(x \right)}}{x^{8}}$$
  7*cosh(x)   7*sinh(x)                    
- --------- - --------- + cosh(x) + sinh(x)
      x           x                        
-------------------------------------------
                      7                    
                     x                     
$$\frac{\sinh{\left(x \right)} + \cosh{\left(x \right)} - \frac{7 \sinh{\left(x \right)}}{x} - \frac{7 \cosh{\left(x \right)}}{x}}{x^{7}}$$
(-7*cosh(x)/x - 7*sinh(x)/x + cosh(x) + sinh(x))/x^7