Answer
$$t=5$$
Work Step by Step
To simplify the equation, you need to determine the least common multiple of $2$, $9$, and $18$. You may do this by prime factorization:
$$2: 2$$ $$9: 3\:x\:3$$ $$18: 2 \:x\: 9 = 2\: x\: 3\: x\: 3$$
Then multiply each factor the greatest number of times it occurs in either number.
$2$ - one occurrence
$3$ - two occurrences
Hence, the LCM would be $2\: x\: 3\: x\: 3$ = $18$
The next step is to multiple both sides by the $LCM =18$ $$\frac{t-4}{2}(18) - \frac{t-3}{9}(18) = \frac{5}{18}(18)$$
Simplifying this will give us: $$9(t-4)-2(t-3)=5$$
Expand: $$9t - 36 - 2t + 6 = 5$$ which is now equal to $$7t - 30 = 5$$
Simplifying further: $$7t = 35$$
Dividing both sides by 7: $$t=5$$
