Question

Giải phương trình:

\(\dfrac{t +3} {t - 2}\) +\(\dfrac{t - 2} { t+3}\) = \(\dfrac{ 5t +15} {t^2 + t -6}\)

MAI HỌC RỒI !! HELP ME /?!/

Answer 1

\(\dfrac{t+3}{t-2}+\dfrac{t-2}{t+3}=\dfrac{5t+15}{t^2+t-6}\)(đkxđ: t khác 2, t khác -3)

<=>\(\dfrac{t+3}{t-2}+\dfrac{t-2}{t+3}=\dfrac{5t+15}{\left(t-2\right)\left(t+3\right)}\)

<=>\(\dfrac{\left(t+3\right)^2}{\left(t-2\right)\left(t+3\right)}+\dfrac{\left(t-2\right)^2}{\left(t+3\right)\left(t-2\right)}=\dfrac{5t+15}{\left(t-2\right)\left(t+3\right)}\)

=>t^2+6t+9+t^2-4t+4=5t+15

<=>2t^2-2t-5t=15-9-4=0

<=>2t^2-7t=0

<=> t(2t-7)=0

<=>t=0

2t-7=0<=>t=-7/2

vậy.....