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ax over b plus cx over d equals e
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[tex]\frac{ax}{b}+\frac{x}{d}=e\ \ \ \ \ \ |multiply\ both\ sides\ by\ "bd"\\\\bd\times\frac{ax}{b}+bd\times\frac{cx}{d}=bde\\\\adx+bcx=bde\\\\(ad+bc)x=bde\ \ \ \ \ |divide\ both\ sides\ by\ (ad+bc)\\\\\boxed{x=\frac{bde}{ad+bc}}[/tex]

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