Question

if a/b=c/d=kthen show thata+c/b+d=a-c/b-d​

Answer 1

Answer:

Proved $\frac{a+c}{b+d} =\frac{a-c}{b-d}$.

Step-by-step explanation:

It is provided that:

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

Then,

a = bk

c = dk

The expression to be proved is:

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

Consider the LHS:

$\frac{a+c}{b+d} =\frac{bk+dk}{b+d}=\frac{k(b+d)}{b+d}=k$

Consider the RHS:

$\frac{a-c}{b-d}=\frac{bk-dk}{b-d}=\frac{k(b-d)}{b-d}=k$

Thus, LHS = RHS.