Question

Solve $\frac{x+5}{6}.\frac{x-3}{9}=\frac{x+2}{12}$.

Answer 1

$\frac{x+5}{6}.\frac{x-3}{9}=\frac{x+12}{12}$

$\Rightarrow \frac{(x+5)(x-3)}{54}=\frac{x+12}{12}$

$\Rightarrow \frac{12(x^2+2x-15)}{54}=x+2$

$\Rightarrow 2x^2+4x-30=9x+18$

$\Rightarrow 2x^2-5x-48=0$

Solving this quadratic equation, we get $x=\frac{5}{4}\pm \frac{\sqrt{409}}{4}$