Question

please solve this question. Challenge for all brainly users give right answer with explanation.​

Answer 1

Question

$\sf \large \dfrac{a}{x} + \dfrac{y}{b} = 1 \: and \: \dfrac{b}{y} + \dfrac{z}{c} = 1$

To Find

$\sf \large \dfrac{x}{a} + \dfrac{c}{z}$

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Correct option is(b) 1

$\sf \longmapsto \dfrac{a}{x} + \dfrac{y}{b} = 1 \: and \: \dfrac{b}{y} + \dfrac{z}{c} = 1$

$\sf \longmapsto \dfrac{a}{x} + \dfrac{y}{b} = 1$

$\sf \longmapsto \dfrac{y}{b} = 1 - \dfrac{a}{x}$

$\sf \longmapsto \dfrac{y}{b} = \dfrac{x - a}{x}$

If we reciprocal the terms of one side we must have to reciprocal the other side's terms also.

$\sf \longmapsto \bold{ \dfrac{b}{y} } = { \red{\dfrac{x}{x - a} }} - - - (1)$

$\sf \longmapsto \dfrac{b}{y} + \dfrac{z}{c} = 1$

$\sf \longmapsto \dfrac{z}{c} = 1 - \dfrac{b}{y}$

$\sf \large\longmapsto \dfrac{z}{c} = 1 - \bigg ( \dfrac{x}{x - a} \bigg )$

$\sf \longmapsto \dfrac{z}{c} = \dfrac{x - a - x}{x - a}$

$\sf \longmapsto \dfrac{z}{c} = \dfrac{ - a}{x - a}$

$\sf \longmapsto \bold{\dfrac{c}{z} }= { \red{\dfrac{x - a}{ - a} }} - - - (2)$

From equation 1 and 2

$\sf \longmapsto{\bold{\green{\bigg( \dfrac{x}{a} + \dfrac{c}{z} \bigg)}}} = \dfrac{x}{a} + \bigg( \dfrac{x - a}{ - a} \bigg )$

$\sf \longmapsto \dfrac{x}{a} + \bigg ( - \dfrac{x}{a} + \dfrac{a}{a} \bigg)$

$\sf = \dfrac{x}{a} - \dfrac{x}{a} + 1 = \bold{1}$

Answer 2

see the attachment

i hope it will help you