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How do you in partial fractions?:
(x^2-x-2)/(x-2)
x^2/(x-2)^2
(x^2)/(1+x)
(((w^2)*25*10^-10)^2+(w*5*10^-5)^2)/(1+(w^2)*25*10^-10)^2
Factor polynomial:
x^4+4*x^3+8*x^2-5*x-10
x^4-4*x^3-7*x^2+22*x+24
x^4-4*x^3-6*x^2+4*x+5
x^4-4*x^3+6*x^2-4*x-15
Least common denominator:
((u^2-4*u+16)/(16*u^2-1)*(4*u^2+u)/(u^3+64)-(u+4)/(4*u^2-u))
m+2/m^2*m-3*m^2/m+2
(m^2+3*m/m^2+3*m+2-m^2-2*m/m^2-2*m-3)/1/m^2-m-6-5/m+1
(m^2+3*m)/(m^2+3*m+2)-(m^2-2*m)/(m^2-2*m-3)
Factor squared:
-y^2+2*y+5
y^2+13*y*a-9*a^2
-y^2-13*y*a-4*a^2
-y^2+13*y*b-2*b^2
Identical expressions
(((w^ two)* twenty-five * ten ^- ten)^ two +(w* five * ten ^- five)^ two)/(one +(w^ two)* twenty-five * ten ^- ten)^ two
(((w squared ) multiply by 25 multiply by 10 to the power of minus 10) squared plus (w multiply by 5 multiply by 10 to the power of minus 5) squared ) divide by (1 plus (w squared ) multiply by 25 multiply by 10 to the power of minus 10) squared
(((w to the power of two) multiply by twenty minus five multiply by ten to the power of minus ten) to the power of two plus (w multiply by five multiply by ten to the power of minus five) to the power of two) divide by (one plus (w to the power of two) multiply by twenty minus five multiply by ten to the power of minus ten) to the power of two
(((w2)*25*10-10)2+(w*5*10-5)2)/(1+(w2)*25*10-10)2
w2*25*10-102+w*5*10-52/1+w2*25*10-102
(((w²)*25*10^-10)²+(w*5*10^-5)²)/(1+(w²)*25*10^-10)²
(((w to the power of 2)*25*10 to the power of -10) to the power of 2+(w*5*10 to the power of -5) to the power of 2)/(1+(w to the power of 2)*25*10 to the power of -10) to the power of 2
(((w^2)2510^-10)^2+(w510^-5)^2)/(1+(w^2)2510^-10)^2
(((w2)2510-10)2+(w510-5)2)/(1+(w2)2510-10)2
w22510-102+w510-52/1+w22510-102
w^22510^-10^2+w510^-5^2/1+w^22510^-10^2
(((w^2)*25*10^-10)^2+(w*5*10^-5)^2) divide by (1+(w^2)*25*10^-10)^2
Similar expressions
(((w^2)*25*10^+10)^2+(w*5*10^-5)^2)/(1+(w^2)*25*10^-10)^2
(((w^2)*25*10^-10)^2-(w*5*10^-5)^2)/(1+(w^2)*25*10^-10)^2
(((w^2)*25*10^-10)^2+(w*5*10^-5)^2)/(1-(w^2)*25*10^-10)^2
(((w^2)*25*10^-10)^2+(w*5*10^-5)^2)/(1+(w^2)*25*10^+10)^2
(((w^2)*25*10^-10)^2+(w*5*10^+5)^2)/(1+(w^2)*25*10^-10)^2

Expression simplification/ Fraction Decomposition into the simple/ (((w^2)*25*10^-10)^2+(w*5*10^-5)^2)/(1+(w^2)*25*10^-10)^2

How do you (((w^2)2510^-10)^2+(w510^-5)^2)/(1+(w^2)2510^-10)^2 in partial fractions?

The solution

You have entered [src]

               2                
/ 2           \                2
\w *25*1.0e-10/  + (w*5*1.0e-5) 
--------------------------------
                         2      
      /     2           \       
      \1 + w *25*1.0e-10/

$$\frac{\left(1.0 \cdot 10^{-10} \cdot 25 w^{2}\right)^{2} + \left(1.0 \cdot 10^{-5} \cdot 5 w\right)^{2}}{\left(1.0 \cdot 10^{-10} \cdot 25 w^{2} + 1\right)^{2}}$$

(((w^2*25)*1.0e-10)^2 + ((w*5)*1.0e-5)^2)/(1 + (w^2*25)*1.0e-10)^2

Fraction decomposition [src]

1.0 - 1.0*(1.0 + 2.5e-9*w^2)/(1.0 + 5.0e-9*w^2 + 6.25e-18*w^4)

$$- \frac{1.0 \left(2.5 \cdot 10^{-9} w^{2} + 1.0\right)}{6.25 \cdot 10^{-18} w^{4} + 5.0 \cdot 10^{-9} w^{2} + 1.0} + 1.0$$

              /              2\    
          1.0*\1.0 + 2.5e-9*w /    
1.0 - -----------------------------
                    2             4
      1.0 + 5.0e-9*w  + 6.25e-18*w

General simplification [src]

 2 /                   2\
w *\2.5e-9 + 6.25e-18*w /
-------------------------
                    2    
     /            2\     
     \1 + 2.5e-9*w /

$$\frac{w^{2} \left(6.25 \cdot 10^{-18} w^{2} + 2.5 \cdot 10^{-9}\right)}{\left(2.5 \cdot 10^{-9} w^{2} + 1\right)^{2}}$$

w^2*(2.5e-9 + 6.25e-18*w^2)/(1 + 2.5e-9*w^2)^2

Numerical answer [src]

(2.5e-9*w^2 + 6.25e-18*w^4)/(1.0 + 2.5e-9*w^2)^2

(2.5e-9*w^2 + 6.25e-18*w^4)/(1.0 + 2.5e-9*w^2)^2

Assemble expression [src]

        2             4
2.5e-9*w  + 6.25e-18*w 
-----------------------
                   2   
    /            2\    
    \1 + 2.5e-9*w /

$$\frac{6.25 \cdot 10^{-18} w^{4} + 2.5 \cdot 10^{-9} w^{2}}{\left(2.5 \cdot 10^{-9} w^{2} + 1\right)^{2}}$$

(2.5e-9*w^2 + 6.25e-18*w^4)/(1 + 2.5e-9*w^2)^2

Combining rational expressions [src]

 2 /                   2\
w *\2.5e-9 + 6.25e-18*w /
-------------------------
                    2    
     /            2\     
     \1 + 2.5e-9*w /

$$\frac{w^{2} \left(6.25 \cdot 10^{-18} w^{2} + 2.5 \cdot 10^{-9}\right)}{\left(2.5 \cdot 10^{-9} w^{2} + 1\right)^{2}}$$

w^2*(2.5e-9 + 6.25e-18*w^2)/(1 + 2.5e-9*w^2)^2

Combinatorics [src]

           2   
   2.5e-9*w    
---------------
              2
1.0 + 2.5e-9*w

$$\frac{2.5 \cdot 10^{-9} w^{2}}{2.5 \cdot 10^{-9} w^{2} + 1.0}$$

2.5e-9*w^2/(1.0 + 2.5e-9*w^2)

Trigonometric part [src]

        2             4
2.5e-9*w  + 6.25e-18*w 
-----------------------
                   2   
    /            2\    
    \1 + 2.5e-9*w /

$$\frac{6.25 \cdot 10^{-18} w^{4} + 2.5 \cdot 10^{-9} w^{2}}{\left(2.5 \cdot 10^{-9} w^{2} + 1\right)^{2}}$$

(2.5e-9*w^2 + 6.25e-18*w^4)/(1 + 2.5e-9*w^2)^2

Rational denominator [src]

        2             4
2.5e-9*w  + 6.25e-18*w 
-----------------------
                   2   
    /            2\    
    \1 + 2.5e-9*w /

$$\frac{6.25 \cdot 10^{-18} w^{4} + 2.5 \cdot 10^{-9} w^{2}}{\left(2.5 \cdot 10^{-9} w^{2} + 1\right)^{2}}$$

(2.5e-9*w^2 + 6.25e-18*w^4)/(1 + 2.5e-9*w^2)^2

Common denominator [src]

              /              2\    
          1.0*\1.0 + 2.5e-9*w /    
1.0 - -----------------------------
                    2             4
      1.0 + 5.0e-9*w  + 6.25e-18*w

$$- \frac{1.0 \left(2.5 \cdot 10^{-9} w^{2} + 1.0\right)}{6.25 \cdot 10^{-18} w^{4} + 5.0 \cdot 10^{-9} w^{2} + 1.0} + 1.0$$

1.0 - 1.0*(1.0 + 2.5e-9*w^2)/(1.0 + 5.0e-9*w^2 + 6.25e-18*w^4)

Powers [src]

        2             4
2.5e-9*w  + 6.25e-18*w 
-----------------------
                   2   
    /            2\    
    \1 + 2.5e-9*w /

$$\frac{6.25 \cdot 10^{-18} w^{4} + 2.5 \cdot 10^{-9} w^{2}}{\left(2.5 \cdot 10^{-9} w^{2} + 1\right)^{2}}$$

(2.5e-9*w^2 + 6.25e-18*w^4)/(1 + 2.5e-9*w^2)^2

Expand expression [src]

             4               2
1.0e-20*625*w  + 1.0e-10*25*w 
------------------------------
                        2     
     /     2           \      
     \1 + w *25*1.0e-10/

$$\frac{1.0 \cdot 10^{-20} \cdot 625 w^{4} + 1.0 \cdot 10^{-10} \cdot 25 w^{2}}{\left(1.0 \cdot 10^{-10} \cdot 25 w^{2} + 1\right)^{2}}$$

(1.0e-20*625*w^4 + 1.0e-10*25*w^2)/(1 + (w^2*25)*1.0e-10)^2

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How do you (((w^2)*25*10^-10)^2+(w*5*10^-5)^2)/(1+(w^2)*25*10^-10)^2 in partial fractions?

The solution

How do you (((w^2)2510^-10)^2+(w510^-5)^2)/(1+(w^2)2510^-10)^2 in partial fractions?