Question

if a/x+y/b=1, b/y+z/c=1, then (x/a+c/z)=?

Answer 1

y/b=1-a/x substituting in 2nd equation and simplifying we get c/z = (a-x)/a c/z + x/a =1

Answer 2

Answer:

$\frac{x}{a}+\frac{c}{z}=1$

Step-by-step explanation:

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

$\implies \frac{a}{x}=1-\frac{y}{b}$

$\implies \frac{x}{a}=\frac{1}{1-\frac{y}{b}}\:--(1)$

$and\:\frac{b}{y}+\frac{z}{c}=1$

$\implies \frac{z}{c}=1-\frac{b}{y}$

$\implies \frac{c}{z}=\frac{1}{1-\frac{b}{y}}\:--(2)$

$Now,\\\frac{x}{a}+\frac{c}{z}=\frac{1}{1-\frac{y}{b}}+\frac{1}{1-\frac{b}{y}}$

$Let \:\frac{y}{b}=m$

$=\frac{1}{1-p}+\frac{1}{1-\frac{1}{m}}\\=\frac{1}{1-m}+\frac{1}{\frac{m-1}{m}}\\=\frac{1}{1-m}-\frac{m}{1-m}\\=\frac{1-m}{1-m}\\=1$

Therefore,

$\frac{x}{a}+\frac{c}{z}=1$

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