Question 337253

Use a common denominator,{{{(t+1)(t-2)}}}
{{{4 - 5/(t+1) = -1/(t-2)}}}
{{{(4(t+1)(t-2))/((t+1)(t-2))-(5(t-2))/((t+1)(t-2))=-1(t+1)/((t+1)(t-2))}}}
{{{(4(t+1)(t-2)-5(t-2)+(t+1))/((t+1)(t-2))=0}}}
{{{(4(t^2-2t+t-2)-5t+10+t+1)/((t+1)(t-2))=0}}}
{{{(4(t^2-t-2)-4t+11)/((t+1)(t-2))=0}}}
{{{(4t^2-4t-8-4t+11)/((t+1)(t-2))=0}}}
{{{(4t^2-8t+3)/((t+1)(t-2))=0}}}
Multiply both side by the common denominator,
{{{4t^2-8t+3=0}}}
Factor
{{{(2t-3)(2t-1)=0}}}
Two solutions:
{{{2t-3=0}}}
{{{2t=3}}}
{{{highlight(t=3/2)}}}
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{{{2t-1=0}}}
{{{2t=1}}}
{{{highlight(t=1/2)}}}