Question 88007
Remember that {{{a/b=c/d}}} means that {{{ad=bc}}}.

Likewise, {{{4/(x+4)= 5/(x-1)}}} means that {{{4(x-1) = 5(x+4) }}}.  This is easy to solve!

 {{{4(x-1) = 5(x+4) }}}
{{{4x-4 = 5x+ 20}}}


Subtract 4x from each side:
{{{4x-4-4x = 5x+20 -4x}}}
{{{-4 = x+20}}}


Subtract 20 from each side:
{{{-4-20=x+20-20}}}
{{{x=-24}}}


Check the answer by substituting the value into the original equation:
{{{4/(x+4)= 5/(x-1)}}}
{{{4/(-24+4)= 5/(-24-1)}}}
{{{4/-20= 5/-25}}}
{{{-1/5=-1/5}}}  It checks!!


R^2