Question 156133
{{{(t-1)/(t+4) = (t-7)/(t+5) + 1}}}
Get rid of the denominators and simplify.
{{{(t-1)cross((t+4))(t+5)/cross((t+4)) = (t-7)(t+4)cross((t+5))/cross((t+5)) + 1(t+4)(t+5)}}}
{{{(t-1)(t+5) = (t-7)(t+4)+ (t+4)(t+5)}}}
{{{(t^2+4t-5) = (t^2-3t-28)+ (t^2+9t+20)}}}
{{{t^2+4t-5 = 2t^2+6t-8}}}
{{{t^2+2t-3=0}}}
Factor the quadratic.
{{{(t+3)(t-1)=0}}}
Two solutions : t=-3,1
Check your answer.
{{{(t-1)/(t+4) = (t-7)/(t+5) + 1}}}
{{{t=1}}}
{{{(1-1)/(1+4) = (1-7)/(1+5) + 1}}}
{{{0 = (-6)/(6) + 1}}}
{{{0=0}}}
I leave it to you to verify the t=-3 solution.