a/ax-1+b/bx-1=-(a+b)

Asked by khushboo panwar | 9th Mar, 2011, 12:00: AM

Expert Answer:

Dear Student,
 
Here is the solution:
 
Multiply by (ax-1)*(bx-1)

a(bx -1) + b(ax-1) = -(a+b)(ax-1) x (bx-1)
2abx - (a + b) = -(a+b)(abx2 - (a+b)x + 1)
2abx = -(a + b)abx2 + x(a+b)2
(a + b)abx2 - (a2 + b2) x = 0

This is a quadratic and can be solved using the standard form for the solution:

X = [-B +/- SQRT(B2 - 4AC)] / 2A

x = [ (a2 + b2) +/- SQRT((a2 + b2)2) ] / [ 2(a + b)ab]
x = [ (a2 + b2) +/- (a2 + b2 ] / [ 2(a + b)ab]

x = 0
x = (a2 + b2) / [ (a + b)ab]

Check: x= 0 yes.
Check: x = (a2 + b2) / [ (a + b)ab]

a/(ax - 1) = a/[(a2 + b2) / [ (a + b)b] - 1]
a/(ax - 1) = a/[(a2 + b2 - (a + b)b) / [ (a + b)b] ]
a/(ax - 1) = a/[(a2 - ab) / [ (a + b)b] ]
a/(ax - 1) = b(a + b)/[(a - b) ]

b/(bx - 1) = b/[(a2 + b2) / [ (a + b)a] - 1]
b/(bx - 1) = a(a + b) / [b - a]

b(a + b)/[(a - b) ] + a(a + b) / [b - a]
(a - b)(a + b)/(b - a) = -(a + b)
-(a + b) = -(a + b) so this checks out OK also
 
Hope this helps
 
Regards
Team Topperlearning

Answered by  | 9th Mar, 2011, 09:12: AM

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