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How do you in partial fractions?:
(a^4-10*a^2+169)/(a^2+6*a+13)
((x+3)/(x-1))^2+14(x^2-9)/(x^2-1)-15((x-3)/(x+1))^2
((x+12)/(x^(3)-9x))/(((x-3)/(2x^2+5x-3))-(9/(9-x^2)))
x-(-1/(1-x)^(1/2))*(1+(-1/((1-x))^(1/2))^2)/(-1/(2*(1-x)^(3/2)))
Factor polynomial:
-x^7+x^6/4+9*x^5/8-9*x^4/32-x^3/8+x^2/32
x^7+4*x^6+4*x^5+2*x^4+4*x^3+3*x^2+3*x+4
x^7-4*x^5+6*x^3-4*x
x^7-3*x^6+8*x^2
Least common denominator:
((u^2-2*u+4)/(4*u^2-1)*(2*u^2+u)/(u^3+8)-(u+2/2*u^2-u))/7/(u^2+2*u)-(10*u+1)/(7-14*u)
t/(t-7)-7/(7-t)
sqrt((x-3)/(x+3))*(x+3)*(1/(2*(x+3))-(x-3)/(2*(x+3)^2))/(x-3)
sqrt(x)*(3*x^2-1/(2*x*sqrt(x)))+(x^3+1/(sqrt(x)))/(2*sqrt(x))
Factor squared:
-y^2-7*y*x-x^2
-y^2-7*y*x-15*x^2
-y^2+7*y*x+7*x^2
y^2-7*y*x+5*x^2
Least common denominator:
(m^2+3*m)/(m^2+3*m+2)-(m^2-2*m)/(m^2-2*m-3)
Identical expressions
(m^ two + three *m)/(m^ two + three *m+ two)-(m^ two - two *m)/(m^ two - two *m- three)
(m squared plus 3 multiply by m) divide by (m squared plus 3 multiply by m plus 2) minus (m squared minus 2 multiply by m) divide by (m squared minus 2 multiply by m minus 3)
(m to the power of two plus three multiply by m) divide by (m to the power of two plus three multiply by m plus two) minus (m to the power of two minus two multiply by m) divide by (m to the power of two minus two multiply by m minus three)
(m2+3*m)/(m2+3*m+2)-(m2-2*m)/(m2-2*m-3)
m2+3*m/m2+3*m+2-m2-2*m/m2-2*m-3
(m²+3*m)/(m²+3*m+2)-(m²-2*m)/(m²-2*m-3)
(m to the power of 2+3*m)/(m to the power of 2+3*m+2)-(m to the power of 2-2*m)/(m to the power of 2-2*m-3)
(m^2+3m)/(m^2+3m+2)-(m^2-2m)/(m^2-2m-3)
(m2+3m)/(m2+3m+2)-(m2-2m)/(m2-2m-3)
m2+3m/m2+3m+2-m2-2m/m2-2m-3
m^2+3m/m^2+3m+2-m^2-2m/m^2-2m-3
(m^2+3*m) divide by (m^2+3*m+2)-(m^2-2*m) divide by (m^2-2*m-3)
Similar expressions
(m^2-3*m)/(m^2+3*m+2)-(m^2-2*m)/(m^2-2*m-3)
(m^2+3*m)/(m^2+3*m+2)+(m^2-2*m)/(m^2-2*m-3)
(m^2+3*m)/(m^2+3*m+2)-(m^2+2*m)/(m^2-2*m-3)
(m^2+3*m)/(m^2+3*m+2)-(m^2-2*m)/(m^2+2*m-3)
(m^2+3*m)/(m^2+3*m+2)-(m^2-2*m)/(m^2-2*m+3)
(m^2+3*m)/(m^2-3*m+2)-(m^2-2*m)/(m^2-2*m-3)
(m^2+3*m)/(m^2+3*m-2)-(m^2-2*m)/(m^2-2*m-3)

Expression simplification/ Fraction Decomposition into the simple/ (m^2+3*m)/(m^2+3*m+2)-(m^2-2*m)/(m^2-2*m-3)

How do you (m^2+3m)/(m^2+3m+2)-(m^2-2m)/(m^2-2m-3) in partial fractions?

The solution

You have entered [src]

   2              2        
  m  + 3*m       m  - 2*m  
------------ - ------------
 2              2          
m  + 3*m + 2   m  - 2*m - 3

$$- \frac{m^{2} - 2 m}{\left(m^{2} - 2 m\right) - 3} + \frac{m^{2} + 3 m}{\left(m^{2} + 3 m\right) + 2}$$

(m^2 + 3*m)/(m^2 + 3*m + 2) - (m^2 - 2*m)/(m^2 - 2*m - 3)

Fraction decomposition [src]

2/(2 + m) - 5/(4*(1 + m)) - 3/(4*(-3 + m))

$$\frac{2}{m + 2} - \frac{5}{4 \left(m + 1\right)} - \frac{3}{4 \left(m - 3\right)}$$

  2         5           3     
----- - --------- - ----------
2 + m   4*(1 + m)   4*(-3 + m)

General simplification [src]

    5*m     
------------
     3      
6 - m  + 7*m

$$\frac{5 m}{- m^{3} + 7 m + 6}$$

5*m/(6 - m^3 + 7*m)

Numerical answer [src]

(m^2 + 3.0*m)/(2.0 + m^2 + 3.0*m) - (m^2 - 2.0*m)/(-3.0 + m^2 - 2.0*m)

(m^2 + 3.0*m)/(2.0 + m^2 + 3.0*m) - (m^2 - 2.0*m)/(-3.0 + m^2 - 2.0*m)

Assemble expression [src]

   2               2        
  m  + 3*m        m  - 2*m  
------------ - -------------
     2               2      
2 + m  + 3*m   -3 + m  - 2*m

$$- \frac{m^{2} - 2 m}{m^{2} - 2 m - 3} + \frac{m^{2} + 3 m}{m^{2} + 3 m + 2}$$

(m^2 + 3*m)/(2 + m^2 + 3*m) - (m^2 - 2*m)/(-3 + m^2 - 2*m)

Rational denominator [src]

/ 2      \ /      2      \   /   2      \ /     2      \
\m  + 3*m/*\-3 + m  - 2*m/ + \- m  + 2*m/*\2 + m  + 3*m/
--------------------------------------------------------
             /      2      \ /     2      \             
             \-3 + m  - 2*m/*\2 + m  + 3*m/

$$\frac{\left(- m^{2} + 2 m\right) \left(m^{2} + 3 m + 2\right) + \left(m^{2} + 3 m\right) \left(m^{2} - 2 m - 3\right)}{\left(m^{2} - 2 m - 3\right) \left(m^{2} + 3 m + 2\right)}$$

((m^2 + 3*m)*(-3 + m^2 - 2*m) + (-m^2 + 2*m)*(2 + m^2 + 3*m))/((-3 + m^2 - 2*m)*(2 + m^2 + 3*m))

Combining rational expressions [src]

m*((-3 + m*(-2 + m))*(3 + m) - (-2 + m)*(2 + m*(3 + m)))
--------------------------------------------------------
           (-3 + m*(-2 + m))*(2 + m*(3 + m))

$$\frac{m \left(- \left(m - 2\right) \left(m \left(m + 3\right) + 2\right) + \left(m + 3\right) \left(m \left(m - 2\right) - 3\right)\right)}{\left(m \left(m - 2\right) - 3\right) \left(m \left(m + 3\right) + 2\right)}$$

m*((-3 + m*(-2 + m))*(3 + m) - (-2 + m)*(2 + m*(3 + m)))/((-3 + m*(-2 + m))*(2 + m*(3 + m)))

Trigonometric part [src]

   2               2        
  m  + 3*m        m  - 2*m  
------------ - -------------
     2               2      
2 + m  + 3*m   -3 + m  - 2*m

$$- \frac{m^{2} - 2 m}{m^{2} - 2 m - 3} + \frac{m^{2} + 3 m}{m^{2} + 3 m + 2}$$

(m^2 + 3*m)/(2 + m^2 + 3*m) - (m^2 - 2*m)/(-3 + m^2 - 2*m)

Common denominator [src]

     -5*m    
-------------
      3      
-6 + m  - 7*m

$$- \frac{5 m}{m^{3} - 7 m - 6}$$

-5*m/(-6 + m^3 - 7*m)

Powers [src]

   2               2        
  m  + 3*m        m  - 2*m  
------------ - -------------
     2               2      
2 + m  + 3*m   -3 + m  - 2*m

$$- \frac{m^{2} - 2 m}{m^{2} - 2 m - 3} + \frac{m^{2} + 3 m}{m^{2} + 3 m + 2}$$

     2             2        
  - m  + 2*m      m  + 3*m  
------------- + ------------
      2              2      
-3 + m  - 2*m   2 + m  + 3*m

$$\frac{- m^{2} + 2 m}{m^{2} - 2 m - 3} + \frac{m^{2} + 3 m}{m^{2} + 3 m + 2}$$

(-m^2 + 2*m)/(-3 + m^2 - 2*m) + (m^2 + 3*m)/(2 + m^2 + 3*m)

Combinatorics [src]

          -5*m          
------------------------
(1 + m)*(-3 + m)*(2 + m)

$$- \frac{5 m}{\left(m - 3\right) \left(m + 1\right) \left(m + 2\right)}$$

-5*m/((1 + m)*(-3 + m)*(2 + m))

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Identical expressions

Similar expressions

How do you (m^2+3*m)/(m^2+3*m+2)-(m^2-2*m)/(m^2-2*m-3) in partial fractions?

The solution

How do you (m^2+3m)/(m^2+3m+2)-(m^2-2m)/(m^2-2m-3) in partial fractions?