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Solution
Given :-
To Prove:-
p : q is the duplicate ratio of (p +r ) :(q + r)
Prove:-
Given Ratio,
= ( p + r ) : (q + r)
= (p + r)/(q + r)
Multiply by r denominator & numerator
= (pr + r²)/( qr + r²)
= (pr + pq)/(qr + pq)
= p(r + q)/q(r + p)
Here, any terms not be cancel by other terms .
So, we can not cancel any terms of here.
So,
= p(r + q)/q(r + p)
That's means,
We can says that p : q is the duplicate ratio of (p + r):(q + r)
That's Proved.
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