HKIMO 2026 Grade 9 National Preliminary Set 01 Question 10

Find $x$: $$\frac{2x}{3+\cfrac4{3+\cfrac4{3+\cfrac4{\ddots}}}}+\frac{3x}{2+\cfrac3{2+\cfrac3{2+\cfrac3{\ddots}}}}=3.$$