Question

apply componendo-dividendo
a/b=2/3​

Answer 1

Answer:

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Step-by-step explanation:

Componendo and Dividendo rule, sometimes called in short C and D rule, says given a proportion [math]\frac{a}{b} = \frac{c}{d}, \frac{a+b}{a-b} = \frac{c+d}{c-d}[/math] is true.

Implicit in this statement are the facts that [math]b ≠ 0, d ≠ 0 , a - b ≠ 0[/math] and [math]c - d ≠ 0[/math].

Basically, C and D rule compactifies multiple manipulations, viz.

[math]\frac{a}{b} = \frac{c}{d} \implies \frac{a}{b} + 1 = \frac{c}{d} + 1 \implies \frac{a+b}{b} = \frac{c+d}{d}[/math] ••••• (I)

[math]\frac{a}{b} = \frac{c}{d} \implies \frac{a}{b} - 1 = \frac{c}{d} - 1 \implies \frac{a-b}{b} = \frac{c-d}{d}[/math] ••••• (II)

Operating [math]\frac{I}{II}[/math] gives C and D rule,

[math]\frac{a+b}{a-b} = \frac{c+d}{c-d}.[/math]