[tex]\it x^2-8x+15 = x^2-3x-5x+15 =x(x-3) - 5(x-3) =
\\ \\
=(x-3)(x-5)[/tex]
[tex]\it x^2-25 =x^2-5^2 = (x-5)(x+5)[/tex]
[tex]\it E(x) = \left[\dfrac{2x-8}{(x-3)(x-5)}-\dfrac{1}{x-3}\right]\cdot(x-5)(x+5) =
\\ \\
\left[\dfrac{\it2x-8}{(x-3)(x-5)}\cdot(x-5)-\dfrac{x-5}{\it x-3}\right]\cdot(\it x+5) =
\\ \\
\it\dfrac{\it2x-8-x+5}{\it x-3}\cdot(\it x+5) =\dfrac{x-3}{x-3}\cdot(\it x+5) =\it x+5[/tex]
