Mister Exam

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How do you in partial fractions?:
z/(2*z-4)-(z^2+4)/(2*z^2-8)-z/(z^2+2*z)
(z-3)/(z+3)*(z+(z^2)/(3-z))
2*(-1+(-1+x)/(2+x))/(2+x)^2
sqrt((w^2*(-t^2)/(1+t^2*w^2))^2+(t*w/(1+t^2*w^2))^2)
Factor polynomial:
m^5-m^3
x^10-1
x^4-x^2+1
x^8+1
Least common denominator:
z/x-z+x+z/z
(z-t)/(z+t)/(z-t)^2
(z/40+1/20)*(z/40+4/5)*z
((z^2-49)/(2*z^2+1))*(((14*z+1)/(z-7))+((14*z-1)/(z+7)))
Factor squared:
-y^4-y^2+15
-y^4-y^2-11
y^4-9*y^2-3
-y^4+y^2+4
Identical expressions
sqrt((w^ two *(-t^ two)/(one +t^ two *w^ two))^ two +(t*w/(one +t^ two *w^ two))^ two)
square root of ((w squared multiply by ( minus t squared ) divide by (1 plus t squared multiply by w squared )) squared plus (t multiply by w divide by (1 plus t squared multiply by w squared )) squared )
square root of ((w to the power of two multiply by ( minus t to the power of two) divide by (one plus t to the power of two multiply by w to the power of two)) to the power of two plus (t multiply by w divide by (one plus t to the power of two multiply by w to the power of two)) to the power of two)
√((w^2*(-t^2)/(1+t^2*w^2))^2+(t*w/(1+t^2*w^2))^2)
sqrt((w2*(-t2)/(1+t2*w2))2+(t*w/(1+t2*w2))2)
sqrtw2*-t2/1+t2*w22+t*w/1+t2*w22
sqrt((w²*(-t²)/(1+t²*w²))²+(t*w/(1+t²*w²))²)
sqrt((w to the power of 2*(-t to the power of 2)/(1+t to the power of 2*w to the power of 2)) to the power of 2+(t*w/(1+t to the power of 2*w to the power of 2)) to the power of 2)
sqrt((w^2(-t^2)/(1+t^2w^2))^2+(tw/(1+t^2w^2))^2)
sqrt((w2(-t2)/(1+t2w2))2+(tw/(1+t2w2))2)
sqrtw2-t2/1+t2w22+tw/1+t2w22
sqrtw^2-t^2/1+t^2w^2^2+tw/1+t^2w^2^2
sqrt((w^2*(-t^2) divide by (1+t^2*w^2))^2+(t*w divide by (1+t^2*w^2))^2)
Similar expressions
sqrt((w^2*(t^2)/(1+t^2*w^2))^2+(t*w/(1+t^2*w^2))^2)
sqrt((w^2*(-t^2)/(1-t^2*w^2))^2+(t*w/(1+t^2*w^2))^2)
sqrt((w^2*(-t^2)/(1+t^2*w^2))^2-(t*w/(1+t^2*w^2))^2)
sqrt((w^2*(-t^2)/(1+t^2*w^2))^2+(t*w/(1-t^2*w^2))^2)

Expression simplification/ Fraction Decomposition into the simple/ sqrt((w^2*(-t^2)/(1+t^2*w^2))^2+(t*w/(1+t^2*w^2))^2)

How do you sqrt((w^2(-t^2)/(1+t^2w^2))^2+(tw/(1+t^2w^2))^2) in partial fractions?

The solution

You have entered [src]

       _____________________________
      /            2                
     /  /  2 /  2\\               2 
    /   | w *\-t /|    /   t*w   \  
   /    |---------|  + |---------|  
  /     |     2  2|    |     2  2|  
\/      \1 + t *w /    \1 + t *w /

$$\sqrt{\left(\frac{t w}{t^{2} w^{2} + 1}\right)^{2} + \left(\frac{- t^{2} w^{2}}{t^{2} w^{2} + 1}\right)^{2}}$$

sqrt(((w^2*(-t^2))/(1 + t^2*w^2))^2 + ((t*w)/(1 + t^2*w^2))^2)

Fraction decomposition [src]

sqrt(t^2*w^2/(1 + t^4*w^4 + 2*t^2*w^2) + t^4*w^4/(1 + t^4*w^4 + 2*t^2*w^2))

$$\sqrt{\frac{t^{4} w^{4}}{t^{4} w^{4} + 2 t^{2} w^{2} + 1} + \frac{t^{2} w^{2}}{t^{4} w^{4} + 2 t^{2} w^{2} + 1}}$$

      ___________________________________________
     /         2  2                  4  4        
    /         t *w                  t *w         
   /   ------------------- + ------------------- 
  /         4  4      2  2        4  4      2  2 
\/     1 + t *w  + 2*t *w    1 + t *w  + 2*t *w

General simplification [src]

      ___________
     /    2  2   
    /    t *w    
   /   --------- 
  /         2  2 
\/     1 + t *w

$$\sqrt{\frac{t^{2} w^{2}}{t^{2} w^{2} + 1}}$$

sqrt(t^2*w^2/(1 + t^2*w^2))

Numerical answer [src]

(t^2*w^2/(1.0 + t^2*w^2)^2 + t^4*w^4/(1.0 + t^2*w^2)^2)^0.5

(t^2*w^2/(1.0 + t^2*w^2)^2 + t^4*w^4/(1.0 + t^2*w^2)^2)^0.5

Powers [src]

       _____________________________
      /     2  2           4  4     
     /     t *w           t *w      
    /   ------------ + ------------ 
   /               2              2 
  /     /     2  2\    /     2  2\  
\/      \1 + t *w /    \1 + t *w /

$$\sqrt{\frac{t^{4} w^{4}}{\left(t^{2} w^{2} + 1\right)^{2}} + \frac{t^{2} w^{2}}{\left(t^{2} w^{2} + 1\right)^{2}}}$$

sqrt(t^2*w^2/(1 + t^2*w^2)^2 + t^4*w^4/(1 + t^2*w^2)^2)

Combining rational expressions [src]

      ___________
     /    2  2   
    /    t *w    
   /   --------- 
  /         2  2 
\/     1 + t *w

$$\sqrt{\frac{t^{2} w^{2}}{t^{2} w^{2} + 1}}$$

sqrt(t^2*w^2/(1 + t^2*w^2))

Expand expression [src]

       _____________________________
      /     2  2           4  4     
     /     t *w           t *w      
    /   ------------ + ------------ 
   /               2              2 
  /     /     2  2\    /     2  2\  
\/      \1 + t *w /    \1 + t *w /

$$\sqrt{\frac{t^{4} w^{4}}{\left(t^{2} w^{2} + 1\right)^{2}} + \frac{t^{2} w^{2}}{\left(t^{2} w^{2} + 1\right)^{2}}}$$

sqrt((t^2*w^2)/(1 + t^2*w^2)^2 + (t^4*w^4)/(1 + t^2*w^2)^2)

Assemble expression [src]

       _____________________________
      /     2  2           4  4     
     /     t *w           t *w      
    /   ------------ + ------------ 
   /               2              2 
  /     /     2  2\    /     2  2\  
\/      \1 + t *w /    \1 + t *w /

$$\sqrt{\frac{t^{4} w^{4}}{\left(t^{2} w^{2} + 1\right)^{2}} + \frac{t^{2} w^{2}}{\left(t^{2} w^{2} + 1\right)^{2}}}$$

sqrt(t^2*w^2/(1 + t^2*w^2)^2 + t^4*w^4/(1 + t^2*w^2)^2)

Common denominator [src]

      ___________
     /    2  2   
    /    t *w    
   /   --------- 
  /         2  2 
\/     1 + t *w

$$\sqrt{\frac{t^{2} w^{2}}{t^{2} w^{2} + 1}}$$

sqrt(t^2*w^2/(1 + t^2*w^2))

Rational denominator [src]

      ___________
     /    2  2   
    /    t *w    
   /   --------- 
  /         2  2 
\/     1 + t *w

$$\sqrt{\frac{t^{2} w^{2}}{t^{2} w^{2} + 1}}$$

sqrt(t^2*w^2/(1 + t^2*w^2))

Trigonometric part [src]

       _____________________________
      /     2  2           4  4     
     /     t *w           t *w      
    /   ------------ + ------------ 
   /               2              2 
  /     /     2  2\    /     2  2\  
\/      \1 + t *w /    \1 + t *w /

$$\sqrt{\frac{t^{4} w^{4}}{\left(t^{2} w^{2} + 1\right)^{2}} + \frac{t^{2} w^{2}}{\left(t^{2} w^{2} + 1\right)^{2}}}$$

sqrt(t^2*w^2/(1 + t^2*w^2)^2 + t^4*w^4/(1 + t^2*w^2)^2)

Combinatorics [src]

      ___________
     /    2  2   
    /    t *w    
   /   --------- 
  /         2  2 
\/     1 + t *w

$$\sqrt{\frac{t^{2} w^{2}}{t^{2} w^{2} + 1}}$$

sqrt(t^2*w^2/(1 + t^2*w^2))

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Similar expressions

How do you sqrt((w^2*(-t^2)/(1+t^2*w^2))^2+(t*w/(1+t^2*w^2))^2) in partial fractions?

The solution

How do you sqrt((w^2(-t^2)/(1+t^2w^2))^2+(tw/(1+t^2w^2))^2) in partial fractions?