Question 207651
{{{2/(t-3)+2/(t-2)=10/(t^2-5t+6)}}} Start with the given equation.



{{{2/(t-3)+2/(t-2)=10/((t-3)(t-2))}}} Factor the last denominator.



{{{cross((t-3))(t-2)(2/cross((t-3)))+(t-3)cross((t-2))(2/cross((t-2)))=cross((t-3)(t-2))(10/(cross((t-3)(t-2))))}}} Multiply EVERY fraction by the LCD {{{(t-3)(t-2)}}} to clear out the fractions.



{{{(t-2)2+(t-3)2=10}}} Simplify



{{{2(t-2)+2(t-3)=10}}} Rearrange the terms.



{{{2t-4+2t-6=10}}} Distribute.



{{{-10+4t=10}}} Combine like terms on the left side.



{{{4t=10+10}}} Add {{{10}}} to both sides.



{{{4t=20}}} Combine like terms on the right side.



{{{t=(20)/(4)}}} Divide both sides by {{{4}}} to isolate {{{t}}}.



{{{t=5}}} Reduce.



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Answer:


So the solution is {{{t=5}}}