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Expression simplification/ Fraction Decomposition into the simple/ 150/(1+150*((15*150)/(151*(1/10p+1))+(15/(260*(5p^2+p)))))

How do you 150/(1+150*((15*150)/(151*(1/10p+1))+(15/(260*(5p^2+p))))) in partial fractions?

An expression to simplify:

The solution

You have entered [src] 
                  150                  
---------------------------------------
        /    2250             15      \
1 + 150*|------------ + --------------|
        |    /p     \       /   2    \|
        |151*|-- + 1|   260*\5*p  + p/|
        \    \10    /                 /
$$\frac{150}{150 \left(\frac{15}{260 \left(5 p^{2} + p\right)} + \frac{2250}{151 \left(\frac{p}{10} + 1\right)}\right) + 1}$$ 
150/(1 + 150*(2250/((151*(p/10 + 1))) + 15/((260*(5*p^2 + p)))))
General simplification [src] 
                  /        2       \         
         588900*p*\10 + 5*p  + 51*p/         
---------------------------------------------
                3                           2
339750 + 19630*p  + 87823235*p + 438950226*p
$$\frac{588900 p \left(5 p^{2} + 51 p + 10\right)}{19630 p^{3} + 438950226 p^{2} + 87823235 p + 339750}$$ 
588900*p*(10 + 5*p^2 + 51*p)/(339750 + 19630*p^3 + 87823235*p + 438950226*p^2)
Fraction decomposition [src] 
150 - 33750*(1510 + 390151*p + 1950000*p^2)/(339750 + 19630*p^3 + 87823235*p + 438950226*p^2)
$$- \frac{33750 \left(1950000 p^{2} + 390151 p + 1510\right)}{19630 p^{3} + 438950226 p^{2} + 87823235 p + 339750} + 150$$ 
                 /                           2\    
           33750*\1510 + 390151*p + 1950000*p /    
150 - ---------------------------------------------
                      3                           2
      339750 + 19630*p  + 87823235*p + 438950226*p
Rational denominator [src] 
                  /        2       \         
         588900*p*\10 + 5*p  + 51*p/         
---------------------------------------------
                3                           2
339750 + 19630*p  + 87823235*p + 438950226*p
$$\frac{588900 p \left(5 p^{2} + 51 p + 10\right)}{19630 p^{3} + 438950226 p^{2} + 87823235 p + 339750}$$ 
588900*p*(10 + 5*p^2 + 51*p)/(339750 + 19630*p^3 + 87823235*p + 438950226*p^2)
Assemble expression [src] 
               150               
---------------------------------
          2250           337500  
1 + --------------- + -----------
                  2         151*p
    260*p + 1300*p    151 + -----
                              10
$$\frac{150}{1 + \frac{2250}{1300 p^{2} + 260 p} + \frac{337500}{\frac{151 p}{10} + 151}}$$ 
150/(1 + 2250/(260*p + 1300*p^2) + 337500/(151 + 151*p/10))
Common denominator [src] 
                                                2  
        50962500 + 13167596250*p + 65812500000*p   
150 - ---------------------------------------------
                      3                           2
      339750 + 19630*p  + 87823235*p + 438950226*p
$$- \frac{65812500000 p^{2} + 13167596250 p + 50962500}{19630 p^{3} + 438950226 p^{2} + 87823235 p + 339750} + 150$$ 
150 - (50962500 + 13167596250*p + 65812500000*p^2)/(339750 + 19630*p^3 + 87823235*p + 438950226*p^2)
Expand expression [src] 
              150               
--------------------------------
         225           337500   
1 + ------------- + ------------
       /   2    \       /p     \
    26*\5*p  + p/   151*|-- + 1|
                        \10    /
$$\frac{150}{1 + \frac{225}{26 \left(5 p^{2} + p\right)} + \frac{337500}{151 \left(\frac{p}{10} + 1\right)}}$$ 
150/(1 + 225/(26*(5*p^2 + p)) + 337500/(151*(p/10 + 1)))
Powers [src] 
               150               
---------------------------------
          2250           337500  
1 + --------------- + -----------
                  2         151*p
    260*p + 1300*p    151 + -----
                              10
$$\frac{150}{1 + \frac{2250}{1300 p^{2} + 260 p} + \frac{337500}{\frac{151 p}{10} + 151}}$$ 
150/(1 + 2250/(260*p + 1300*p^2) + 337500/(151 + 151*p/10))
Combinatorics [src] 
         588900*p*(1 + 5*p)*(10 + p)         
---------------------------------------------
                3                           2
339750 + 19630*p  + 87823235*p + 438950226*p
$$\frac{588900 p \left(p + 10\right) \left(5 p + 1\right)}{19630 p^{3} + 438950226 p^{2} + 87823235 p + 339750}$$ 
588900*p*(1 + 5*p)*(10 + p)/(339750 + 19630*p^3 + 87823235*p + 438950226*p^2)
Trigonometric part [src] 
               150               
---------------------------------
          2250           337500  
1 + --------------- + -----------
                  2         151*p
    260*p + 1300*p    151 + -----
                              10
$$\frac{150}{1 + \frac{2250}{1300 p^{2} + 260 p} + \frac{337500}{\frac{151 p}{10} + 151}}$$ 
150/(1 + 2250/(260*p + 1300*p^2) + 337500/(151 + 151*p/10))
Combining rational expressions [src] 
                    588900*p*(1 + 5*p)*(10 + p)                    
-------------------------------------------------------------------
339750 + 33975*p + 87750000*p*(1 + 5*p) + 3926*p*(1 + 5*p)*(10 + p)
$$\frac{588900 p \left(p + 10\right) \left(5 p + 1\right)}{3926 p \left(p + 10\right) \left(5 p + 1\right) + 87750000 p \left(5 p + 1\right) + 33975 p + 339750}$$ 
588900*p*(1 + 5*p)*(10 + p)/(339750 + 33975*p + 87750000*p*(1 + 5*p) + 3926*p*(1 + 5*p)*(10 + p))
Numerical answer [src] 
150.0/(1.0 + 2250.0/(260.0*p + 1300.0*p^2) + 337500.0/(151.0 + 15.1*p))
150.0/(1.0 + 2250.0/(260.0*p + 1300.0*p^2) + 337500.0/(151.0 + 15.1*p))
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