Let's check your solution by starting from the top:
Given the expression:
[tex]\text{ }\frac{15}{a^2-1}\text{ = }\frac{5}{2a\text{ - 2}}[/tex]
Let's simplify. We get,
[tex]\text{ }\frac{15}{a^2-1}\text{ = }\frac{5}{2a\text{ - 2}}[/tex][tex]\text{ }(15)(2a\text{ -2) = }(5)(a^2\text{ -1)}[/tex][tex]\text{ 30a - 30 = 5a}^2\text{ - 5}[/tex][tex]\text{5a}^2\text{ - 5 - 30a + 30 = 0}[/tex][tex]\text{5a}^2\text{ - 30a + 25 = 0}[/tex][tex](\text{5a}^2\text{ - 30a + 25 = 0)(}\frac{1}{5})[/tex][tex]\text{ a}^2\text{ - 6a + 5 = 0}[/tex][tex]\text{ (a - 1)(a - 5) = 0}[/tex]
