[tex]\dfrac{ax}{b}+\dfrac{cx}{d}=e\\\\\dfrac{ax\cdot d}{b\cdot d}+\dfrac{cx\cdot b}{d\cdot b}=e\\\\\dfrac{adx}{bd}+\dfrac{bcx}{bd}=e\\\\\dfrac{adx+bcx}{bd}=e\qquad|\cdot bd\neq0\\\\adx+bcx=bde\qquad|\text{factor out the variable x}\\\\x(ad+bc)=bde\qquad|\text{divide both sides by}\ (ad+bc)\neq0\\\\\boxed{x=\dfrac{bde}{ad+bc}}[/tex]
