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How do you in partial fractions?:
(z-(5*z)/z+1)/(z-4)/(z+1)
1/(1+x^2/3)
(x^2-5*x+6)/(x-3)
((z^2-49)/(2*z^2+1))*(((14*z+1)/(z-7))+((14*z-1)/(z+7)))
Factor polynomial:
y^3+y^5
x^3-x
x1^2+x2^2
x^3+7*x^2+15*x+9
Least common denominator:
(x*(x-6)^2)^(1/3)*((x-6)^2/3+x*(-12+2*x)/3)/(x*(x-6)^2)
(2*a+b)/(a^2-b^2)+1/(a+b)
(z/(z-1))+((z^2-1.0923*z)/(z^2-1.9061*z+0.9277))
(a+1/a+2)/a+1
Factor squared:
y^4+y^2-3
y^4+y^2+4
y^4-12*y^2+7
y^2+4*y-3
Least common denominator:
((z^2-49)/(2*z^2+1))*(((14*z+1)/(z-7))+((14*z-1)/(z+7)))
Identical expressions
((z^ two - forty-nine)/(two *z^ two + one))*(((fourteen *z+ one)/(z- seven))+((fourteen *z- one)/(z+ seven)))
((z squared minus 49) divide by (2 multiply by z squared plus 1)) multiply by (((14 multiply by z plus 1) divide by (z minus 7)) plus ((14 multiply by z minus 1) divide by (z plus 7)))
((z to the power of two minus forty minus nine) divide by (two multiply by z to the power of two plus one)) multiply by (((fourteen multiply by z plus one) divide by (z minus seven)) plus ((fourteen multiply by z minus one) divide by (z plus seven)))
((z2-49)/(2*z2+1))*(((14*z+1)/(z-7))+((14*z-1)/(z+7)))
z2-49/2*z2+1*14*z+1/z-7+14*z-1/z+7
((z²-49)/(2*z²+1))*(((14*z+1)/(z-7))+((14*z-1)/(z+7)))
((z to the power of 2-49)/(2*z to the power of 2+1))*(((14*z+1)/(z-7))+((14*z-1)/(z+7)))
((z^2-49)/(2z^2+1))(((14z+1)/(z-7))+((14z-1)/(z+7)))
((z2-49)/(2z2+1))(((14z+1)/(z-7))+((14z-1)/(z+7)))
z2-49/2z2+114z+1/z-7+14z-1/z+7
z^2-49/2z^2+114z+1/z-7+14z-1/z+7
((z^2-49) divide by (2*z^2+1))*(((14*z+1) divide by (z-7))+((14*z-1) divide by (z+7)))
Similar expressions
((z^2-49)/(2*z^2+1))*(((14*z+1)/(z+7))+((14*z-1)/(z+7)))
((z^2+49)/(2*z^2+1))*(((14*z+1)/(z-7))+((14*z-1)/(z+7)))
((z^2-49)/(2*z^2+1))*(((14*z-1)/(z-7))+((14*z-1)/(z+7)))
((z^2-49)/(2*z^2+1))*(((14*z+1)/(z-7))+((14*z-1)/(z-7)))
((z^2-49)/(2*z^2-1))*(((14*z+1)/(z-7))+((14*z-1)/(z+7)))
((z^2-49)/(2*z^2+1))*(((14*z+1)/(z-7))-((14*z-1)/(z+7)))
((z^2-49)/(2*z^2+1))*(((14*z+1)/(z-7))+((14*z+1)/(z+7)))

Expression simplification/ Fraction Decomposition into the simple/ ((z^2-49)/(2*z^2+1))*(((14*z+1)/(z-7))+((14*z-1)/(z+7)))

How do you ((z^2-49)/(2z^2+1))(((14z+1)/(z-7))+((14z-1)/(z+7))) in partial fractions?

The solution

You have entered [src]

 2                            
z  - 49  /14*z + 1   14*z - 1\
--------*|-------- + --------|
   2     \ z - 7      z + 7  /
2*z  + 1

$$\frac{z^{2} - 49}{2 z^{2} + 1} \left(\frac{14 z - 1}{z + 7} + \frac{14 z + 1}{z - 7}\right)$$

((z^2 - 49)/(2*z^2 + 1))*((14*z + 1)/(z - 7) + (14*z - 1)/(z + 7))

Fraction decomposition [src]

$$14$$

General simplification [src]

$$14$$

Rational denominator [src]

/       2\                                            
\-49 + z /*((1 + 14*z)*(7 + z) + (-1 + 14*z)*(-7 + z))
------------------------------------------------------
             /       2\                               
             \1 + 2*z /*(-7 + z)*(7 + z)

$$\frac{\left(z^{2} - 49\right) \left(\left(z - 7\right) \left(14 z - 1\right) + \left(z + 7\right) \left(14 z + 1\right)\right)}{\left(z - 7\right) \left(z + 7\right) \left(2 z^{2} + 1\right)}$$

(-49 + z^2)*((1 + 14*z)*(7 + z) + (-1 + 14*z)*(-7 + z))/((1 + 2*z^2)*(-7 + z)*(7 + z))

Assemble expression [src]

/       2\ /1 + 14*z   -1 + 14*z\
\-49 + z /*|-------- + ---------|
           \ -7 + z      7 + z  /
---------------------------------
                    2            
             1 + 2*z

$$\frac{\left(z^{2} - 49\right) \left(\frac{14 z - 1}{z + 7} + \frac{14 z + 1}{z - 7}\right)}{2 z^{2} + 1}$$

(-49 + z^2)*((1 + 14*z)/(-7 + z) + (-1 + 14*z)/(7 + z))/(1 + 2*z^2)

Trigonometric part [src]

/       2\ /1 + 14*z   -1 + 14*z\
\-49 + z /*|-------- + ---------|
           \ -7 + z      7 + z  /
---------------------------------
                    2            
             1 + 2*z

$$\frac{\left(z^{2} - 49\right) \left(\frac{14 z - 1}{z + 7} + \frac{14 z + 1}{z - 7}\right)}{2 z^{2} + 1}$$

(-49 + z^2)*((1 + 14*z)/(-7 + z) + (-1 + 14*z)/(7 + z))/(1 + 2*z^2)

Common denominator [src]

$$14$$

Powers [src]

/       2\ /1 + 14*z   -1 + 14*z\
\-49 + z /*|-------- + ---------|
           \ -7 + z      7 + z  /
---------------------------------
                    2            
             1 + 2*z

$$\frac{\left(z^{2} - 49\right) \left(\frac{14 z - 1}{z + 7} + \frac{14 z + 1}{z - 7}\right)}{2 z^{2} + 1}$$

(-49 + z^2)*((1 + 14*z)/(-7 + z) + (-1 + 14*z)/(7 + z))/(1 + 2*z^2)

Combining rational expressions [src]

/       2\                                            
\-49 + z /*((1 + 14*z)*(7 + z) + (-1 + 14*z)*(-7 + z))
------------------------------------------------------
             /       2\                               
             \1 + 2*z /*(-7 + z)*(7 + z)

$$\frac{\left(z^{2} - 49\right) \left(\left(z - 7\right) \left(14 z - 1\right) + \left(z + 7\right) \left(14 z + 1\right)\right)}{\left(z - 7\right) \left(z + 7\right) \left(2 z^{2} + 1\right)}$$

(-49 + z^2)*((1 + 14*z)*(7 + z) + (-1 + 14*z)*(-7 + z))/((1 + 2*z^2)*(-7 + z)*(7 + z))

Numerical answer [src]

(-49.0 + z^2)*((-1.0 + 14.0*z)/(7.0 + z) + (1.0 + 14.0*z)/(-7.0 + z))/(1.0 + 2.0*z^2)

(-49.0 + z^2)*((-1.0 + 14.0*z)/(7.0 + z) + (1.0 + 14.0*z)/(-7.0 + z))/(1.0 + 2.0*z^2)

Combinatorics [src]

$$14$$

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How do you ((z^2-49)/(2*z^2+1))*(((14*z+1)/(z-7))+((14*z-1)/(z+7))) in partial fractions?

The solution

How do you ((z^2-49)/(2z^2+1))(((14z+1)/(z-7))+((14z-1)/(z+7))) in partial fractions?