(4x^2-1)/(16x^2)-1+(1)/(2x+1)+(1)/(2x-1)+(1)/(1-4x^2) (x+y)/(xy)-(2)/(x)(xy)/(x^2)-y^(2)

1. The given expression is $\frac {4x^{2}-1}{16x^{2}-1}+\frac {1}{2x+1}+\frac {1}{2x-1}+\frac {1}{1-4x^{2}}$. To simplify this expression, we can factor the numerators and denominators where possible. The expression simplifies to $\frac{1}{(2x + 1)(2x - 1)} + \frac{1}{2x + 1} + \frac{1}{2x - 1} + \frac{1}{1 - 4x^2}$.<br /><br />2. The second expression is $\frac {x+y}{xy}-\frac {2}{x}\frac {xy}{x^{2}-y^{2}}$. To simplify this expression, we can factor out common terms and cancel them out. The expression simplifies to $\frac{x + y}{x y} - \frac{2}{x} \times \frac{x y}{(x - y)(x + y)}$.<br /><br />Both expressions involve algebraic manipulation, including factoring, simplifying fractions, and canceling out common terms. These are common tasks in algebra, a branch of mathematics.