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Question Number 207381 by efronzo1 last updated on 13/May/24

Answered by mr W last updated on 13/May/24

((BD∙CE)/(AC∙DE)) =(((BE+DE)∙CE)/((AE+CE)∙DE)) =(((((BE)/(DE))+1)∙CE)/((((AE)/(CE))+1)∙DE)) =((((BC)/(AD))+1)/(((BC)/(AD))+1)) =((x+1)/(x+1))=1

$$\frac{{BD}\centerdot{CE}}{{AC}\centerdot{DE}} \\ $$$$=\frac{\left({BE}+{DE}\right)\centerdot{CE}}{\left({AE}+{CE}\right)\centerdot{DE}} \\ $$$$=\frac{\left(\frac{{BE}}{{DE}}+\mathrm{1}\right)\centerdot{CE}}{\left(\frac{{AE}}{{CE}}+\mathrm{1}\right)\centerdot{DE}} \\ $$$$=\frac{\frac{{BC}}{{AD}}+\mathrm{1}}{\frac{{BC}}{{AD}}+\mathrm{1}} \\ $$$$=\frac{{x}+\mathrm{1}}{{x}+\mathrm{1}}=\mathrm{1} \\ $$

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