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How do you in partial fractions?:
(x^3+12*x)*(x/(2*(x^3+12*x))+(-12-3*x^2)*(x^2+4)/(4*(x^3+12*x)^2))/(x^2+4)
(6x^2+29x)/(x+5)
(x^2+2x-15)/(x+5)
(t^4+9)/(t^4+9t^2)
Factor polynomial:
m^3+m^2+m+1-m^4-m^3-m^2-m-1
0.09-a^2
x^5-x^7/7
x^8-y^6
Least common denominator:
((-k2/p)*(k3/(t3*p+1))+k1*p)*((k5*p)/(1+k3*p*(k3/(t3*p+1))*(k4*(t4*p+1))))
((x*x-11*x+30)/(x*x-9*x+20))/((x*x-36)/(x*x-16))
k1/(1+k1*(-k2*k3*k3/((t3^2*s^2+2*t3*s*e+1)*(t2*s+1))+1/(t1*s+1)))
(k1*p*(k4*(t4*p+1))+k2/p)*k5*p+(k1*p)*(k3/(t3*p+1))
Factor squared:
-8*p^2+6*p+1
2*p^2+3*p-2
-y^4-14*y^2-2
y^4+y^2-8
Least common denominator:
(x^3+12*x)*(x/(2*(x^3+12*x))+(-12-3*x^2)*(x^2+4)/(4*(x^3+12*x)^2))/(x^2+4)
Identical expressions
(x^ three + twelve *x)*(x/(two *(x^ three + twelve *x))+(- twelve - three *x^ two)*(x^ two + four)/(four *(x^ three + twelve *x)^ two))/(x^ two + four)
(x cubed plus 12 multiply by x) multiply by (x divide by (2 multiply by (x cubed plus 12 multiply by x)) plus ( minus 12 minus 3 multiply by x squared ) multiply by (x squared plus 4) divide by (4 multiply by (x cubed plus 12 multiply by x) squared )) divide by (x squared plus 4)
(x to the power of three plus twelve multiply by x) multiply by (x divide by (two multiply by (x to the power of three plus twelve multiply by x)) plus ( minus twelve minus three multiply by x to the power of two) multiply by (x to the power of two plus four) divide by (four multiply by (x to the power of three plus twelve multiply by x) to the power of two)) divide by (x to the power of two plus four)
(x3+12*x)*(x/(2*(x3+12*x))+(-12-3*x2)*(x2+4)/(4*(x3+12*x)2))/(x2+4)
x3+12*x*x/2*x3+12*x+-12-3*x2*x2+4/4*x3+12*x2/x2+4
(x³+12*x)*(x/(2*(x³+12*x))+(-12-3*x²)*(x²+4)/(4*(x³+12*x)²))/(x²+4)
(x to the power of 3+12*x)*(x/(2*(x to the power of 3+12*x))+(-12-3*x to the power of 2)*(x to the power of 2+4)/(4*(x to the power of 3+12*x) to the power of 2))/(x to the power of 2+4)
(x^3+12x)(x/(2(x^3+12x))+(-12-3x^2)(x^2+4)/(4(x^3+12x)^2))/(x^2+4)
(x3+12x)(x/(2(x3+12x))+(-12-3x2)(x2+4)/(4(x3+12x)2))/(x2+4)
x3+12xx/2x3+12x+-12-3x2x2+4/4x3+12x2/x2+4
x^3+12xx/2x^3+12x+-12-3x^2x^2+4/4x^3+12x^2/x^2+4
(x^3+12*x)*(x divide by (2*(x^3+12*x))+(-12-3*x^2)*(x^2+4) divide by (4*(x^3+12*x)^2)) divide by (x^2+4)
Similar expressions
(x^3+12*x)*(x/(2*(x^3+12*x))-(-12-3*x^2)*(x^2+4)/(4*(x^3+12*x)^2))/(x^2+4)
(x^3+12*x)*(x/(2*(x^3+12*x))+(12-3*x^2)*(x^2+4)/(4*(x^3+12*x)^2))/(x^2+4)
(x^3+12*x)*(x/(2*(x^3+12*x))+(-12-3*x^2)*(x^2-4)/(4*(x^3+12*x)^2))/(x^2+4)
(x^3+12*x)*(x/(2*(x^3+12*x))+(-12-3*x^2)*(x^2+4)/(4*(x^3-12*x)^2))/(x^2+4)
(x^3+12*x)*(x/(2*(x^3+12*x))+(-12-3*x^2)*(x^2+4)/(4*(x^3+12*x)^2))/(x^2-4)
(x^3+12*x)*(x/(2*(x^3-12*x))+(-12-3*x^2)*(x^2+4)/(4*(x^3+12*x)^2))/(x^2+4)
(x^3+12*x)*(x/(2*(x^3+12*x))+(-12+3*x^2)*(x^2+4)/(4*(x^3+12*x)^2))/(x^2+4)
(x^3-12*x)*(x/(2*(x^3+12*x))+(-12-3*x^2)*(x^2+4)/(4*(x^3+12*x)^2))/(x^2+4)

Expression simplification/ Fraction Decomposition into the simple/ (x^3+12*x)*(x/(2*(x^3+12*x))+(-12-3*x^2)*(x^2+4)/(4*(x^3+12*x)^2))/(x^2+4)

How do you (x^3+12x)(x/(2(x^3+12x))+(-12-3x^2)(x^2+4)/(4(x^3+12x)^2))/(x^2+4) in partial fractions?

The solution

You have entered [src]

            /                /         2\ / 2    \\
/ 3       \ |      x         \-12 - 3*x /*\x  + 4/|
\x  + 12*x/*|------------- + ---------------------|
            |  / 3       \                    2   |
            |2*\x  + 12*x/         / 3       \    |
            \                    4*\x  + 12*x/    /
---------------------------------------------------
                        2                          
                       x  + 4

$$\frac{\left(x^{3} + 12 x\right) \left(\frac{x}{2 \left(x^{3} + 12 x\right)} + \frac{\left(- 3 x^{2} - 12\right) \left(x^{2} + 4\right)}{4 \left(x^{3} + 12 x\right)^{2}}\right)}{x^{2} + 4}$$

((x^3 + 12*x)*(x/((2*(x^3 + 12*x))) + ((-12 - 3*x^2)*(x^2 + 4))/((4*(x^3 + 12*x)^2))))/(x^2 + 4)

General simplification [src]

      /      4\      
     -\48 + x /      
---------------------
    /      4       2\
4*x*\48 + x  + 16*x /

$$- \frac{x^{4} + 48}{4 x \left(x^{4} + 16 x^{2} + 48\right)}$$

-(48 + x^4)/(4*x*(48 + x^4 + 16*x^2))

Fraction decomposition [src]

-1/(4*x) + x/(2*(4 + x^2)) - x/(2*(12 + x^2))

$$- \frac{x}{2 \left(x^{2} + 12\right)} + \frac{x}{2 \left(x^{2} + 4\right)} - \frac{1}{4 x}$$

   1        x             x     
- --- + ---------- - -----------
  4*x     /     2\     /      2\
        2*\4 + x /   2*\12 + x /

Numerical answer [src]

(x^3 + 12.0*x)*(x/(2.0*x^3 + 24.0*x) + 0.00173611111111111*(4.0 + x^2)*(-12.0 - 3.0*x^2)/(x + 0.0833333333333333*x^3)^2)/(4.0 + x^2)

(x^3 + 12.0*x)*(x/(2.0*x^3 + 24.0*x) + 0.00173611111111111*(4.0 + x^2)*(-12.0 - 3.0*x^2)/(x + 0.0833333333333333*x^3)^2)/(4.0 + x^2)

Combining rational expressions [src]

   2 /      2\     /      2\ /     2\
2*x *\12 + x / + 3*\-4 - x /*\4 + x /
-------------------------------------
            /     2\ /      2\       
        4*x*\4 + x /*\12 + x /

$$\frac{2 x^{2} \left(x^{2} + 12\right) + 3 \left(- x^{2} - 4\right) \left(x^{2} + 4\right)}{4 x \left(x^{2} + 4\right) \left(x^{2} + 12\right)}$$

(2*x^2*(12 + x^2) + 3*(-4 - x^2)*(4 + x^2))/(4*x*(4 + x^2)*(12 + x^2))

Combinatorics [src]

      /      4\       
     -\48 + x /       
----------------------
    /     2\ /      2\
4*x*\4 + x /*\12 + x /

$$- \frac{x^{4} + 48}{4 x \left(x^{2} + 4\right) \left(x^{2} + 12\right)}$$

-(48 + x^4)/(4*x*(4 + x^2)*(12 + x^2))

Common denominator [src]

     /      4\      
    -\48 + x /      
--------------------
   5       3        
4*x  + 64*x  + 192*x

$$- \frac{x^{4} + 48}{4 x^{5} + 64 x^{3} + 192 x}$$

-(48 + x^4)/(4*x^5 + 64*x^3 + 192*x)

Trigonometric part [src]

            /              /         2\ /     2\\
/ 3       \ |     x        \-12 - 3*x /*\4 + x /|
\x  + 12*x/*|----------- + ---------------------|
            |   3                           2   |
            |2*x  + 24*x         / 3       \    |
            \                  4*\x  + 12*x/    /
-------------------------------------------------
                           2                     
                      4 + x

$$\frac{\left(x^{3} + 12 x\right) \left(\frac{x}{2 x^{3} + 24 x} + \frac{\left(- 3 x^{2} - 12\right) \left(x^{2} + 4\right)}{4 \left(x^{3} + 12 x\right)^{2}}\right)}{x^{2} + 4}$$

(x^3 + 12*x)*(x/(2*x^3 + 24*x) + (-12 - 3*x^2)*(4 + x^2)/(4*(x^3 + 12*x)^2))/(4 + x^2)

Powers [src]

            /              /         2\ /     2\\
/ 3       \ |     x        \-12 - 3*x /*\4 + x /|
\x  + 12*x/*|----------- + ---------------------|
            |   3                           2   |
            |2*x  + 24*x         / 3       \    |
            \                  4*\x  + 12*x/    /
-------------------------------------------------
                           2                     
                      4 + x

$$\frac{\left(x^{3} + 12 x\right) \left(\frac{x}{2 x^{3} + 24 x} + \frac{\left(- 3 x^{2} - 12\right) \left(x^{2} + 4\right)}{4 \left(x^{3} + 12 x\right)^{2}}\right)}{x^{2} + 4}$$

(x^3 + 12*x)*(x/(2*x^3 + 24*x) + (-12 - 3*x^2)*(4 + x^2)/(4*(x^3 + 12*x)^2))/(4 + x^2)

Assemble expression [src]

            /              /         2\ /     2\\
/ 3       \ |     x        \-12 - 3*x /*\4 + x /|
\x  + 12*x/*|----------- + ---------------------|
            |   3                           2   |
            |2*x  + 24*x         / 3       \    |
            \                  4*\x  + 12*x/    /
-------------------------------------------------
                           2                     
                      4 + x

$$\frac{\left(x^{3} + 12 x\right) \left(\frac{x}{2 x^{3} + 24 x} + \frac{\left(- 3 x^{2} - 12\right) \left(x^{2} + 4\right)}{4 \left(x^{3} + 12 x\right)^{2}}\right)}{x^{2} + 4}$$

(x^3 + 12*x)*(x/(2*x^3 + 24*x) + (-12 - 3*x^2)*(4 + x^2)/(4*(x^3 + 12*x)^2))/(4 + x^2)

Rational denominator [src]

               2                                      
    / 3       \    /         2\ /     2\ /   3       \
4*x*\x  + 12*x/  + \-12 - 3*x /*\4 + x /*\2*x  + 24*x/
------------------------------------------------------
           /     2\ / 3       \ /   3       \         
         4*\4 + x /*\x  + 12*x/*\2*x  + 24*x/

$$\frac{4 x \left(x^{3} + 12 x\right)^{2} + \left(- 3 x^{2} - 12\right) \left(x^{2} + 4\right) \left(2 x^{3} + 24 x\right)}{4 \left(x^{2} + 4\right) \left(x^{3} + 12 x\right) \left(2 x^{3} + 24 x\right)}$$

(4*x*(x^3 + 12*x)^2 + (-12 - 3*x^2)*(4 + x^2)*(2*x^3 + 24*x))/(4*(4 + x^2)*(x^3 + 12*x)*(2*x^3 + 24*x))

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Identical expressions

Similar expressions

How do you (x^3+12*x)*(x/(2*(x^3+12*x))+(-12-3*x^2)*(x^2+4)/(4*(x^3+12*x)^2))/(x^2+4) in partial fractions?

The solution

How do you (x^3+12x)(x/(2(x^3+12x))+(-12-3x^2)(x^2+4)/(4(x^3+12x)^2))/(x^2+4) in partial fractions?