Find Common Denominator: First, find a common denominator for all terms to eliminate the fractions.Common denominator for 4,3 is 12.Multiply each term by 12 to clear the fractions:12×(43t−2)−12×(32t+3)=12×(32)−12×t
Clear Fractions: Simplify each term:(412)⋅(3t−2)−(312)⋅(2t+3)=(212)−12t3⋅(3t−2)−4⋅(2t+3)=6−12t
Simplify Terms: Distribute and combine like terms:9t−6−8t−12=8−12tt−18=8−12t
Combine Like Terms: Add 12t to both sides to get all t terms on one side:t+12t−18=813t−18=8
Isolate Term with t: Add 18 to both sides to isolate the term with t:13t=26
Solve for t: Divide both sides by 13 to solve for t:t = 1326t = 2
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