Question

(a-b)÷(a+b)=x, then fins the ratio of a and b

Answer 1

Answer:

Componendo and dividendo

In this law if a : b : : c : d than (a + b) : (a – b) : : (c + d) : (c – d). Thus, when using together you have to apply components in the numerator and dividend in the numerator.

By applying componendo and dividendo

= $\frac{a-b}{a+b}$ = x

= $\frac{a-b+a+b}{a-b+a+b}$ = $\frac{x+1}{x-1}$

= $\frac{2a}{2b}$ = $\frac{x+1}{x-1}$

∴ $\frac{a}{b}$ = = $\frac{x+1}{x-1}$