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Answer:
(2x +1)/(4x^2) . . . . except x=0, -1
Step-by-step explanation:
Addition of fractions works in the usual way:
a/b +c/d = (ad +bc)/(bd)
Division of fractions works in the usual way:
(a/b)/(c/d) = (ad)/(bc)
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[tex]\dfrac{\left(\dfrac{1}{2x}+\dfrac{1}{2x+2}\right)}{\left(\dfrac{2x}{x+1}\right)}=\dfrac{1}{2}\cdot\dfrac{\left(\dfrac{1}{x}+\dfrac{1}{x+1}\right)}{\left(\dfrac{2x}{x+1}\right)}=\dfrac{1}{2}\cdot\dfrac{\left(\dfrac{2x+1}{x(x+1)}\right)}{\left(\dfrac{2x^2}{x(x+1)}\right)}\\\\=\boxed{\dfrac{2x+1}{4x^2}}[/tex]
The expression is undefined for any denominator equal to zero: x=0 or x=-1.
