Question

1/x-1/x+b=1/a-1/a+b , x=not 0 ,-b

Answer 1

Hey

Put x = a , and we clearly have one soln.

 [tex] \frac{1}{x} - \frac{1}{x+b} = \frac{1}{a} - \frac{1}{a+b} \\ \\ \frac{b}{x(x+b)} = \frac{b}{a(a+b)} \\ \\ x^2 + bx = a^2 + ab \\ \\ ( x + a )( x - a ) = -b ( x - a ) \\ \\ x = a \ \ \ \ \ x = - b - a[/tex]