[tex]\begin{gathered} \frac{1}{x} - \frac{1}{x - b} = \frac{1}{a} - \frac{1}{a - b} \\ there \: are \: two \: possibilities \\ 1 \\ x = a \: \: \: \: x - b = a - b \\ x = a \\ 2 \\ x = - (a - b) \: \: \: \: \: \: - (x - b) = a \\ x = b - a \\ therefore \: x = a \: \: \: x = b - a\end{gathered}[/tex]
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Explanation:
[tex]\begin{gathered} \frac{1}{x} - \frac{1}{x - b} = \frac{1}{a} - \frac{1}{a - b} \\ there \: are \: two \: possibilities \\ 1 \\ x = a \: \: \: \: x - b = a - b \\ x = a \\ 2 \\ x = - (a - b) \: \: \: \: \: \: - (x - b) = a \\ x = b - a \\ therefore \: x = a \: \: \: x = b - a\end{gathered}[/tex]
[tex] \frac{1}{x} - \frac{1}{x - b} = \frac{1}{a} - \frac{1}{a - b} \\ \\ [/tex]
There are two possibilities 1
[tex]x = a \: \: x - b = a - b \\ \\ x = a \\ \\ 2[/tex]
Therefore, x = a x= b - a