a÷x-a÷b=b÷x-b÷a what is the solution of this simple equation
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a/x - a/b = b/x - b/a
or,a/x - b/x = a/b - b/a
or,a - b/x = a² - b²/ab
or,a - b/x = (a+b) (a-b) / ab
or,x(a+b) = ab
∴x= ab/a+b
or,a/x - b/x = a/b - b/a
or,a - b/x = a² - b²/ab
or,a - b/x = (a+b) (a-b) / ab
or,x(a+b) = ab
∴x= ab/a+b
tiasaghosh5876:
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after puting brackets it becomes,
(a÷ x)-(a÷ b)=(b ÷x) -(b ÷a)
after LCM
(ab-ax)÷bx= (ab-xb)÷ax
a(ab-ax)=b(ab-bx)
a²b-a²x =ab²-b²x
b²x -a²x =ab²- a²b
x(b² -a²)= ab(b-a)
x(b-a)(b+a)=ab(b-a)
x=ab/(a+b)
(a÷ x)-(a÷ b)=(b ÷x) -(b ÷a)
after LCM
(ab-ax)÷bx= (ab-xb)÷ax
a(ab-ax)=b(ab-bx)
a²b-a²x =ab²-b²x
b²x -a²x =ab²- a²b
x(b² -a²)= ab(b-a)
x(b-a)(b+a)=ab(b-a)
x=ab/(a+b)
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