Answer
$\dfrac{5x+2}{x^{2}-1}+\dfrac{3}{x^{2}+x}-\dfrac{1}{x^{2}-x}=\dfrac{5x^{2}+4x-4}{x(x+1)(x-1)}$
Work Step by Step
$\dfrac{5x+2}{x^{2}-1}+\dfrac{3}{x^{2}+x}-\dfrac{1}{x^{2}-x}$
Factor the denominators of all three fractions:
$\dfrac{5x+2}{x^{2}-1}+\dfrac{3}{x^{2}+x}-\dfrac{1}{x^{2}-x}=...$
$...=\dfrac{5x+2}{(x-1)(x+1)}+\dfrac{3}{x(x+1)}-\dfrac{1}{x(x-1)}=...$
Evaluate the indicated operations using the LCD, which is $x(x-1)(x+1)$ in this case:
$...=\dfrac{(5x+2)(x)+3(x-1)-(x+1)}{x(x+1)(x-1)}=...$
Simplify:
$...=\dfrac{5x^{2}+2x+3x-3-x-1}{x(x+1)(x-1)}=...$
$...=\dfrac{5x^{2}+4x-4}{x(x+1)(x-1)}$
