Answer
$x=\dfrac{13}{12}$
Work Step by Step
$\log_{5}(x+1)-\log_{5}(x-1)=2$
Combine the logarithms on the left side of the equation as a division:
$\log_{5}\Big(\dfrac{x+1}{x-1}\Big)=2$
Write this equation in exponential form:
$\Big(\dfrac{x+1}{x-1}\Big)=5^{2}$
$\Big(\dfrac{x+1}{x-1}\Big)=25$
Solve for $x$:
$x+1=25(x-1)$
$x+1=25x-25$
$x-25x=-25-1$
$-24x=-26$
$x=\dfrac{-26}{-24}=\dfrac{13}{12}$