Question

a/x-b + b/x-a = 2 give me answer quickly

Answer 1

Answer:

x= a+b, a+b/2

Step-by-step explanation:

a/x-b + b/x-a = 2

Multiplicity both sides by LCM (x-b)(x-a)

a(x-a)+b(x-b) = 2 (x-b)(x-a)

[a(x-a)+b(x-b)]=2[ (x-b)(x-a ]

ax-a²+bx-b²= 2(x²-ax-bx+ab)

ax-a²+bx-b²=2x²-2ax-2bx+2ab

2x²-3ax-3bx+a²+b²+2ab=0

2x²-3(a+b)x+(a+b)² =0

2x²-2(a+b)x - (a+b)x+(a+b)² =0

2x[ x-(a+b) ] -(a+b)[ x-(a+b) }

2x(x-a-b)-(a+b)( x-a-b)=0

(x-a-b)(2x-a-b)=0

so x-a-b=0

x=a+b

or 2x-a-b=0,

2x=a+b,

x=(a+b)/2

hence x= a+b, a+b/2