Unclear: 3÷2t-2+4=2t÷3t-3
To eliminate ambiguity, it's essential that you use parentheses:
3/(2t-2) + 4 = 2t/(3t-3)
First: obtain the LCD. The denominator 2t-2 equals 2(t-1); 3t-3 equals 3(t-1).
The LCD is then 2(3)(t-1).
Multiply each of the terms of 3/(2t-2) + 4 = 2t/(3t-3) by the LCD, obtaining
9 + 4(2)(3)(t-1) = (2t)(2).
Thus, 9 + 24(t-1) = 4t, or 9 + 24t - 24 = 4t
Combining like terms: 24t-4t = 24-9 = 15, or 20t = 15, or t=3/4
It's important that you check this result. Let t=3/4 in the original equation. Is the equation still true?