solve for x: a/ax-1 + b/bx-1 = a+b, where x is not = 1/a, 1/b. a+b is not = 0, ab is not = 0
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step-1 : a/ax-1 +b/bx-1 = a+b
step-2 : a/ax-1 - b = a - b/bx-1
step-3 : a-abx+b/ax-1=abx-a-b/bx-1
step-4 : a-abx+b/-(a-abx+b)=ax-1/bx-1
step-5 : -1=ax-1/bx-1
step-6 : -bx+1=ax-1
step-7 : -bx-ax=-1-1
step-8 : -x(a+b)=-2
step-9 : x=2/a+b
step-2 : a/ax-1 - b = a - b/bx-1
step-3 : a-abx+b/ax-1=abx-a-b/bx-1
step-4 : a-abx+b/-(a-abx+b)=ax-1/bx-1
step-5 : -1=ax-1/bx-1
step-6 : -bx+1=ax-1
step-7 : -bx-ax=-1-1
step-8 : -x(a+b)=-2
step-9 : x=2/a+b
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