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If $a/b=c/d$, then which of the following does not hold good?

1. $(a+b)/b=(c+d)/d$
2. $(a+c)/(b+d)=(a-c)/(b-d)$
3. $(a+b)/(a-b)=(c+d)/(c-d)$
4. $(a+c)/(b-d)=(a-c)(b+d)$

### 1 comment

D?

A. $\frac{a}{b}$ = $\frac{c}{d}$ $\Rightarrow$ $\frac{a}{b}$ + 1 = $\frac{c}{d}$ + 1 $\Rightarrow$ $\frac{a+b}{b}$ = $\frac{c+d}{d}$ ✔

B. $\frac{a}{b}$ = $\frac{c}{d}$ $\Rightarrow$ $\frac{a}{c}$ = $\frac{b}{d}$

Using Componendo, $\frac{a+c}{c}$ = $\frac{b+d}{d}$

Using Dividendo, $\frac{a-c}{c}$ = $\frac{b-d}{d}$

By dividing both, we get $\frac{a+c}{a-c}$ = $\frac{b+d}{b-d}$ $\Rightarrow$ $\frac{a+c}{b+d}$ = $\frac{a-c}{b-d}$ ✔

C. $\frac{a}{b}$ = $\frac{c}{d}$

Using Componendo, $\frac{a+b}{b}$ = $\frac{c+d}{d}$

Using Dividendo, $\frac{a-b}{b}$ = $\frac{c-d}{d}$

By dividing both, we get $\frac{a+b}{a-b}$ = $\frac{c+d}{c-d}$ ✔

Try by taking some values and evaluate them in options, you will get answer,

for e.g take, a=4, b=2, c=16, d=8