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Question Number 207576 by efronzo1 last updated on 19/May/24

Commented by A5T last updated on 19/May/24

$$4$$

Commented by mr W last updated on 19/May/24

$$whend=c:\frac{a}{b}=\frac{6x}{2x}=3$$$$\Rightarrow \frac{a}{b}+\frac{c}{d}=3+1=4$$

Answered by mr W last updated on 19/May/24

Commented by mr W last updated on 19/May/24

$$generalcase:$$$$let\lambda =\frac{y}{x}$$$$\frac{k}{d}=\frac{nx-y}{mx}=\frac{n-\lambda }{m}$$$$\frac{c}{k}=\frac{a}{b}=\frac{mx+nx}{mx+nx-y}=\frac{m+n}{m+n-\lambda }$$$$\frac{k}{d}\times \frac{c}{k}=\frac{c}{d}=\left(\frac{n-\lambda }{m}\right)\frac{a}{b}$$$$\Rightarrow \frac{c}{d}+\frac{a}{b}=\left(\frac{m+n-\lambda }{m}\right)\frac{a}{b}$$$$=\left(\frac{m+n-\lambda }{m}\right)\times \left(\frac{m+n}{m+n-\lambda }\right)$$$$=\frac{m+n}{m}=\frac{2+6}{2}=4✓$$

Commented by Tawa11 last updated on 21/Jun/24

$$\mathrm{weldone}\mathrm{sir}$$

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