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How to use it?
Least common denominator:
sqrt(x)*exp(x/2)/2+exp(x/2)/(2*sqrt(x))
sqrt(x)*(5/x+3*sqrt(x)/2)+(5*log(x)+x^(3/2))/(2*sqrt(x))
sqrt(x^3/(2-x))*(2-x)*(x^3/(2*(2-x)^2)+3*x^2/(2*(2-x)))/x^3
sqrt(x*(2-x))/2+sqrt(x*(2-x))*(1-x)*(3+x)/(2*x*(2-x))
Factor polynomial:
x^n-2*x^n-3*x
x^n-2*x^2*x^n+2
x^9+x^8+x^7+x^5+x^4+x^2
x+9*x^4
Factor squared:
-y^2+y+8
y^2+y-8
-y^2+9*y+5
y^2-9*y-5
How do you in partial fractions?:
(x^2-8*x+15)/(x^2-25)
(x+1-1/1-x)/(x-x2/x-1)
(w*i*0.00005)/(1+w*i*0.00005)
tg(7/(sqrt(3(n^4+2))))
How do you in partial fractions?:
sqrt(((x^2+1)/(x^4-79*x^2+4))^2+(-9*x/(x^4-79*x^2+4))^2)
Identical expressions
sqrt(((x^ two + one)/(x^ four - seventy-nine *x^ two + four))^ two +(- nine *x/(x^ four - seventy-nine *x^ two + four))^ two)
square root of (((x squared plus 1) divide by (x to the power of 4 minus 79 multiply by x squared plus 4)) squared plus ( minus 9 multiply by x divide by (x to the power of 4 minus 79 multiply by x squared plus 4)) squared )
square root of (((x to the power of two plus one) divide by (x to the power of four minus seventy minus nine multiply by x to the power of two plus four)) to the power of two plus ( minus nine multiply by x divide by (x to the power of four minus seventy minus nine multiply by x to the power of two plus four)) to the power of two)
√(((x^2+1)/(x^4-79*x^2+4))^2+(-9*x/(x^4-79*x^2+4))^2)
sqrt(((x2+1)/(x4-79*x2+4))2+(-9*x/(x4-79*x2+4))2)
sqrtx2+1/x4-79*x2+42+-9*x/x4-79*x2+42
sqrt(((x²+1)/(x⁴-79*x²+4))²+(-9*x/(x⁴-79*x²+4))²)
sqrt(((x to the power of 2+1)/(x to the power of 4-79*x to the power of 2+4)) to the power of 2+(-9*x/(x to the power of 4-79*x to the power of 2+4)) to the power of 2)
sqrt(((x^2+1)/(x^4-79x^2+4))^2+(-9x/(x^4-79x^2+4))^2)
sqrt(((x2+1)/(x4-79x2+4))2+(-9x/(x4-79x2+4))2)
sqrtx2+1/x4-79x2+42+-9x/x4-79x2+42
sqrtx^2+1/x^4-79x^2+4^2+-9x/x^4-79x^2+4^2
sqrt(((x^2+1) divide by (x^4-79*x^2+4))^2+(-9*x divide by (x^4-79*x^2+4))^2)
Similar expressions
sqrt(((x^2+1)/(x^4-79*x^2+4))^2-(-9*x/(x^4-79*x^2+4))^2)
sqrt(((x^2+1)/(x^4-79*x^2+4))^2+(-9*x/(x^4+79*x^2+4))^2)
sqrt(((x^2-1)/(x^4-79*x^2+4))^2+(-9*x/(x^4-79*x^2+4))^2)
sqrt(((x^2+1)/(x^4-79*x^2-4))^2+(-9*x/(x^4-79*x^2+4))^2)
sqrt(((x^2+1)/(x^4-79*x^2+4))^2+(-9*x/(x^4-79*x^2-4))^2)
sqrt(((x^2+1)/(x^4-79*x^2+4))^2+(9*x/(x^4-79*x^2+4))^2)
sqrt(((x^2+1)/(x^4+79*x^2+4))^2+(-9*x/(x^4-79*x^2+4))^2)

Expression simplification/ Least common denominator/ sqrt(((x^2+1)/(x^4-79*x^2+4))^2+(-9*x/(x^4-79*x^2+4))^2)

Least common denominator sqrt(((x^2+1)/(x^4-79x^2+4))^2+(-9x/(x^4-79*x^2+4))^2)

The solution

You have entered [src]

       _______________________________________
      /                 2                     
     /  /     2        \                    2 
    /   |    x  + 1    |    /     -9*x     \  
   /    |--------------|  + |--------------|  
  /     | 4       2    |    | 4       2    |  
\/      \x  - 79*x  + 4/    \x  - 79*x  + 4/

$$\sqrt{\left(\frac{\left(-1\right) 9 x}{\left(x^{4} - 79 x^{2}\right) + 4}\right)^{2} + \left(\frac{x^{2} + 1}{\left(x^{4} - 79 x^{2}\right) + 4}\right)^{2}}$$

sqrt(((x^2 + 1)/(x^4 - 79*x^2 + 4))^2 + ((-9*x)/(x^4 - 79*x^2 + 4))^2)

Fraction decomposition [src]

sqrt(1/(16 + x^8 - 632*x^2 - 158*x^6 + 6249*x^4) + x^4/(16 + x^8 - 632*x^2 - 158*x^6 + 6249*x^4) + 83*x^2/(16 + x^8 - 632*x^2 - 158*x^6 + 6249*x^4))

$$\sqrt{\frac{x^{4}}{x^{8} - 158 x^{6} + 6249 x^{4} - 632 x^{2} + 16} + \frac{83 x^{2}}{x^{8} - 158 x^{6} + 6249 x^{4} - 632 x^{2} + 16} + \frac{1}{x^{8} - 158 x^{6} + 6249 x^{4} - 632 x^{2} + 16}}$$

      _________________________________________________________________________________________________________________
     /                                                         4                                      2                
    /                   1                                     x                                   83*x                 
   /   ----------------------------------- + ----------------------------------- + ----------------------------------- 
  /          8        2        6         4         8        2        6         4         8        2        6         4 
\/     16 + x  - 632*x  - 158*x  + 6249*x    16 + x  - 632*x  - 158*x  + 6249*x    16 + x  - 632*x  - 158*x  + 6249*x

General simplification [src]

        ___________________
       /         2         
      /  /     2\        2 
     /   \1 + x /  + 81*x  
    /    ----------------- 
   /                     2 
  /      /     4       2\  
\/       \4 + x  - 79*x /

$$\sqrt{\frac{81 x^{2} + \left(x^{2} + 1\right)^{2}}{\left(x^{4} - 79 x^{2} + 4\right)^{2}}}$$

sqrt(((1 + x^2)^2 + 81*x^2)/(4 + x^4 - 79*x^2)^2)

Numerical answer [src]

0.113924050632911*(x^2/(0.0506329113924051 - x^2 + 0.0126582278481013*x^4)^2 + 0.0123456790123457*(1.0 + x^2)^2/(0.0506329113924051 - x^2 + 0.0126582278481013*x^4)^2)^0.5

0.113924050632911*(x^2/(0.0506329113924051 - x^2 + 0.0126582278481013*x^4)^2 + 0.0123456790123457*(1.0 + x^2)^2/(0.0506329113924051 - x^2 + 0.0126582278481013*x^4)^2)^0.5

Expand expression [src]

        _______________________________________
       /             2                         
      /      / 2    \                  2       
     /       \x  + 1/              81*x        
    /    ----------------- + ----------------- 
   /                     2                   2 
  /      / 4       2    \    / 4       2    \  
\/       \x  - 79*x  + 4/    \x  - 79*x  + 4/

$$\sqrt{\frac{81 x^{2}}{\left(\left(x^{4} - 79 x^{2}\right) + 4\right)^{2}} + \frac{\left(x^{2} + 1\right)^{2}}{\left(\left(x^{4} - 79 x^{2}\right) + 4\right)^{2}}}$$

sqrt((x^2 + 1)^2/(x^4 - 79*x^2 + 4)^2 + (81*x^2)/(x^4 - 79*x^2 + 4)^2)

Rational denominator [src]

        ___________________
       /         2         
      /  /     2\        2 
     /   \1 + x /  + 81*x  
    /    ----------------- 
   /                     2 
  /      / 4       2    \  
\/       \x  - 79*x  + 4/

$$\sqrt{\frac{81 x^{2} + \left(x^{2} + 1\right)^{2}}{\left(\left(x^{4} - 79 x^{2}\right) + 4\right)^{2}}}$$

sqrt(((1 + x^2)^2 + 81*x^2)/(x^4 - 79*x^2 + 4)^2)

Assemble expression [src]

        _______________________________________
       /             2                         
      /      /     2\                  2       
     /       \1 + x /              81*x        
    /    ----------------- + ----------------- 
   /                     2                   2 
  /      /     4       2\    /     4       2\  
\/       \4 + x  - 79*x /    \4 + x  - 79*x /

$$\sqrt{\frac{81 x^{2}}{\left(x^{4} - 79 x^{2} + 4\right)^{2}} + \frac{\left(x^{2} + 1\right)^{2}}{\left(x^{4} - 79 x^{2} + 4\right)^{2}}}$$

sqrt((1 + x^2)^2/(4 + x^4 - 79*x^2)^2 + 81*x^2/(4 + x^4 - 79*x^2)^2)

Trigonometric part [src]

        _______________________________________
       /             2                         
      /      /     2\                  2       
     /       \1 + x /              81*x        
    /    ----------------- + ----------------- 
   /                     2                   2 
  /      /     4       2\    /     4       2\  
\/       \4 + x  - 79*x /    \4 + x  - 79*x /

$$\sqrt{\frac{81 x^{2}}{\left(x^{4} - 79 x^{2} + 4\right)^{2}} + \frac{\left(x^{2} + 1\right)^{2}}{\left(x^{4} - 79 x^{2} + 4\right)^{2}}}$$

sqrt((1 + x^2)^2/(4 + x^4 - 79*x^2)^2 + 81*x^2/(4 + x^4 - 79*x^2)^2)

Combinatorics [src]

      _____________________________________
     /                 4       2           
    /             1 + x  + 83*x            
   /   ----------------------------------- 
  /          8        2        6         4 
\/     16 + x  - 632*x  - 158*x  + 6249*x

$$\sqrt{\frac{x^{4} + 83 x^{2} + 1}{x^{8} - 158 x^{6} + 6249 x^{4} - 632 x^{2} + 16}}$$

sqrt((1 + x^4 + 83*x^2)/(16 + x^8 - 632*x^2 - 158*x^6 + 6249*x^4))

Powers [src]

        _______________________________________
       /             2                         
      /      /     2\                  2       
     /       \1 + x /              81*x        
    /    ----------------- + ----------------- 
   /                     2                   2 
  /      /     4       2\    /     4       2\  
\/       \4 + x  - 79*x /    \4 + x  - 79*x /

$$\sqrt{\frac{81 x^{2}}{\left(x^{4} - 79 x^{2} + 4\right)^{2}} + \frac{\left(x^{2} + 1\right)^{2}}{\left(x^{4} - 79 x^{2} + 4\right)^{2}}}$$

sqrt((1 + x^2)^2/(4 + x^4 - 79*x^2)^2 + 81*x^2/(4 + x^4 - 79*x^2)^2)

Common denominator [src]

      _________________________________________________________________________________________________________________
     /                                                         4                                      2                
    /                   1                                     x                                   83*x                 
   /   ----------------------------------- + ----------------------------------- + ----------------------------------- 
  /          8        2        6         4         8        2        6         4         8        2        6         4 
\/     16 + x  - 632*x  - 158*x  + 6249*x    16 + x  - 632*x  - 158*x  + 6249*x    16 + x  - 632*x  - 158*x  + 6249*x

$$\sqrt{\frac{x^{4}}{x^{8} - 158 x^{6} + 6249 x^{4} - 632 x^{2} + 16} + \frac{83 x^{2}}{x^{8} - 158 x^{6} + 6249 x^{4} - 632 x^{2} + 16} + \frac{1}{x^{8} - 158 x^{6} + 6249 x^{4} - 632 x^{2} + 16}}$$

sqrt(1/(16 + x^8 - 632*x^2 - 158*x^6 + 6249*x^4) + x^4/(16 + x^8 - 632*x^2 - 158*x^6 + 6249*x^4) + 83*x^2/(16 + x^8 - 632*x^2 - 158*x^6 + 6249*x^4))

Combining rational expressions [src]

        ______________________
       /          2           
      /   /     2\        2   
     /    \1 + x /  + 81*x    
    /    -------------------- 
   /                        2 
  /      /     2 /       2\\  
\/       \4 + x *\-79 + x //

$$\sqrt{\frac{81 x^{2} + \left(x^{2} + 1\right)^{2}}{\left(x^{2} \left(x^{2} - 79\right) + 4\right)^{2}}}$$

sqrt(((1 + x^2)^2 + 81*x^2)/(4 + x^2*(-79 + x^2))^2)

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How to use it?

Identical expressions

Similar expressions

Least common denominator sqrt(((x^2+1)/(x^4-79*x^2+4))^2+(-9*x/(x^4-79*x^2+4))^2)

The solution

Least common denominator sqrt(((x^2+1)/(x^4-79x^2+4))^2+(-9x/(x^4-79*x^2+4))^2)