Question 124748
{{{(x^2+ 7x)/(x^2-5x) + (x^2 -4x)/(x^2-5x)}}}     


 {{{((x^2+ 7x)(x^2-5x) + (x^2 -4x)(x^2-5x))/(x^2-5x) (x^2-5x) }}}   


{{{(x^4 - 5x^3 + 7x^3 -35x^2 + x^4 -5x^3 -4x^3 +20x^2)/(x^2-5x)(x^2-5x) }}}         


{{{(2x^4 -7x^3 -15x^2 )/(x^4-5x^3-5x^3+25x^2) }}} 


{{{(2x^4 -7x^3 -15x^2 )/(x^4-10x^3+25x^2) }}} 


{{{x^2(2x^2 -7x -15 )/x^2(x^2-10x+25) }}}  


{{{cross(x^2)(2x^2 -2x -15 )/cross(x^2)(x^2-10x+25) }}} 


 {{{(2x^2 -7x -15 )/(x^2-10x+25) }}} 

now factor out {{{2x^2 -7x -15}}} and {{{x^2-10x+25}}}

{{{2x^2 -7x -15}}}......... replace {{{-7x}}} with {{{3x -10x}}} 

{{{2x^2 + 3x -10x-15}}}......... 

{{{(2x^2 + 3x) -(10x+15)}}}......... 

{{{x(2x + 3) -5(2x+3)}}}......... 

{{{ (x-5)(2x+3) }}}.........

other one will be: 

{{{x^2-10x+25}}}............replace {{{ -10x}}} with {{{ -5x -5x}}} 

{{{x^2 -5x -5x+25}}}............

{{{(x^2 -5x) -(5x-25)}}}............

{{{x(x -5) -5(x-5)}}}............

{{{ (x -5)(x-5) }}}............


substitute them in:{{{(2x^2 -7x -15 )/(x^2-10x+25) }}} 

{{{((x-5)(2x+3))/((x -5)(x-5)) }}} 


{{{(cross((x-5))(2x+3))/(cross((x -5))(x-5)) }}} 

{{{(2x+3)/(x-5) }}}