Question

if (a-x) : (b-x) be duplicate ratio if a : b show that 1/x = 1/a + 1/b

Answer 1

(a-x):(b-x)=a:b, a-x=a and b-x=b, so x=0
(a-x)/(b-x)=a/b
a(b-x)=b(a-x)
ab-ax=ab-bx
ab-ab-ax=-bx
-ax=-bx
ax=bx
a=b

Answer 2

Answer:

Step-by-step explanation:

The question means that a-x:b-x=a²:b²

=>b²(a-x)=a²(b-x)

=>b²a-b²x=a²b-a²x

=>b²a-a²b=b²x-a²x

=>ab(b-a)=x(b²-a²)

=>ab(b-a)=x(b+a)(b-a)

=>ab=x(a+b)

=>1/x=a+b/ab

=>1/x=a/ab+b/ab

=>1/x=1/a+1/b

Hence proved