Question 109172
Please help me with this problem.

 x+5       (x^2+10x+25        10x)
----    /   ---------   *  -----------
x+10        (x^2+10x      x^2+15x+50)

 


 

x+5       (x^2+10x+25        10x)
----    /   ---------   *  -----------
x+10        (x^2+10x      x^2+15x+50)


I hope you need to write your problem this way:

{{{((x+5)/(x+10))/(((x^2+10x+25)/ (x^2+10x))*(10x/(x^2+15x+50))) )}}}

now we can fator  {{{(x^2+10x+25)}}} like this:

 {{{ x^2+5x + 5x +25)}}}...group first two terms and second two terms:

{{{(x^2 + 5x) + (5x + 25) = x(x+5) + 5(x+5) = (x+5)(x+5)}}}....substitute this in previous expression:

{{{((x+5)/(x+10))/(((x+5)(x+5)/ (x^2+10x))*(10x/(x^2+15x+50))) )}}}

now we can fator  {{{(x^2+15x+50)= x^2 + 10x + 5x + 50= (x^2 + 10x) + (5x + 50) = x(x + 10) + 5(x + 10) = (x+10)(x+5)}}}, and factor this {{{(x^2+10x)= x(x+10)}}} substitute both in previous expression:

{{{((x+5)/(x+10))/(((x+5)(x+5)/ x(x+10))*(10x/(x+10)(x+5)))) )}}}

in denominator you can cancel {{{x}}} and {{{x+5}}}


   {{{((x+5)/(x+10))/(((x+5)/ (x+10))*(10/(x+10)))) )}}}...multiply terms in denominator


    {{{((x+5)/(x+10))/((10(x+5)/ (x+10)(x+10)))) )}}}....now product of inner and outer terms


{{{((x+5)(x+10)(x+10))/(10(x+5)(x + 10))}}}....cancel {{{x+5}}} and {{{x + 10}}}
 

{{{(x+10)/10}}}....



Or, if you need to write your problem like this:

{{{(((x+5)/(x+10))/((x^2+10x+25)/ (x^2+10x)))*(10x/(x^2+15x+50) )}}}     


{{{((x+5)(x^2+10x)/(x+10)(x^2+10x+25))*(10x/(x^2+15x+50) )}}}     

now we can fator this: 
{{{x^2+10x= x(x + 10)}}}....

and this:{{{x^2+10x+25=(x+5)(x+5)}}}....

and this:  {{{(x^2+15x+50)= (x+10)(x+5)}}}....

now substitute it in previous expression:

{{{(x(x+10)(x+5)/(x+10)(x+5)(x+5))*(10x/(x+10)(x+5) )}}} ...cancel {{{x+10}}} and {{{x+5}}}
    
{{{10x*x/(x+10)(x+5)(x+5)) )}}} 

{{{10x^2/(x+10)(x+5)(x+5)) )}}}