Question

if a:b = c:d , Prove that a-b/a+b = c-d/c+d​

Answer 1

$\star\:\:\:\sf\large\underline\blue{Question:-}$

• Prove the following.

$\star\:\:\:\sf\large\underline\blue{Proof:-}$

Given that,

$\sf a \colon b = c \colon d$

$\sf \implies \frac{a}{b} = \frac{c}{d}$

Adding 1 to both side, we get,

$\sf \implies \frac{a}{b} + 1= \frac{c}{d} + 1$

$\sf \implies \frac{a + b}{b} = \frac{c + d}{d} \: ...(i)$

Again,

$\sf \frac{a}{b} = \frac{c}{d}$

Subtracting 1 from both side, we get,

$\sf \implies \frac{a}{b} - 1 = \frac{c}{d} - 1$

$\sf \implies \frac{a - b}{b} = \frac{c - d}{d} \: ...(ii)$

Now, dividing (i) by (ii), we get,

$\sf \implies \large \frac{ \frac{a + b}{ \cancel{b}} }{ \frac{a - b}{ \cancel{b}} } = \frac{ \frac{c + d}{ \cancel{d}} }{ \frac{c - d}{ \cancel{d}} }$

$\sf \implies \frac{a + b}{a - b} = \frac{c + d}{c - d}$

Hence Proved.

Answer 2

Answer:

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