Question

2/3(t-5) -1/4(t-2) =1​

Answer 1

$\frac{2}{3(t - 5)} - \frac{1}{4(t - 2)} = 1 \\ \\ \frac{2}{3t - 15} - \frac{1}{4t - 8} = 1 \\ \\ \frac{2(4t - 8) - 1(3t - 15)}{(3t - 15)(4t - 8)} = 1 \\ \\ \frac{8t - 16 - (3t - 15)}{3t(4t - 8) - 15(4t - 8)} = 1 \\ \\ \frac{8t - 16 - 3t + 15}{12 {t}^{2} - 24t - (60t - 120)} = 1 \\ \\ \frac{8t - 3t - 16 + 15}{12 {t }^{2} - 24t - 60t + 120} = 1 \\ \\ \frac{5t - 1}{ 12{t}^{2} - 84t + 120} = 1 \\ \\ 5t - 1 = 12 {t}^{2} - 84t + 120 \\ \\ 5t - 1 = 12 {t}^{2} - 60t - 24t + 120 \\ \\ 5t - 1 = 12t(t - 5) - 24(t - 5) \\ \\ 5t - 1 = (12t - 24)(t - 5)$