Answer:
-2-[tex]\frac{2}{a}[/tex]
Step-by-step explanation:
I broke up the fractions so that it is easier.
[tex]\frac{1}{a-1}[/tex] - [tex]\frac{1}{a+1}[/tex] - [tex]\frac{2}{2a+1}[/tex] - [tex]\frac{2}{2a-1}[/tex] = ([tex]\frac{1}{a}[/tex] - [tex]\frac{1}{1}[/tex]) - ([tex]\frac{1}{a}[/tex] + [tex]\frac{1}{1}[/tex]) - ([tex]\frac{2}{2a}[/tex] + [tex]\frac{2}{1}[/tex]) - ([tex]\frac{2}{2a}[/tex] - [tex]\frac{2}{1}[/tex])
Now I remove the brackets. One plus and one minus make one minus and two minus makes one plus.
([tex]\frac{1}{a}[/tex] - [tex]\frac{1}{1}[/tex]) - ([tex]\frac{1}{a}[/tex] + [tex]\frac{1}{1}[/tex]) - ([tex]\frac{2}{2a}[/tex] + [tex]\frac{2}{1}[/tex]) - ([tex]\frac{2}{2a}[/tex] - [tex]\frac{2}{1}[/tex]) =[tex]\frac{1}{a}[/tex] - [tex]\frac{1}{1}[/tex] - [tex]\frac{1}{a}[/tex] - [tex]\frac{1}{1}[/tex] - [tex]\frac{2}{2a}[/tex] - [tex]\frac{2}{1}[/tex] - [tex]\frac{2}{2a}[/tex] + [tex]\frac{2}{1}[/tex]
Remove redundancies. ([tex]\frac{1}{a}[/tex] - [tex]\frac{1}{a}[/tex] = 0)
[tex]\frac{1}{a}[/tex] - [tex]\frac{1}{1}[/tex] - [tex]\frac{1}{a}[/tex] - [tex]\frac{1}{1}[/tex] - [tex]\frac{2}{2a}[/tex] - [tex]\frac{2}{1}[/tex] - [tex]\frac{2}{2a}[/tex] + [tex]\frac{2}{1}[/tex] = -[tex]\frac{2}{1}[/tex] -[tex]\frac{4}{2a}[/tex]
Simplify the fractions.
-[tex]\frac{2}{1}[/tex] -[tex]\frac{4}{2a}[/tex] = -2-[tex]\frac{2}{a}[/tex]
