Question #9daa9

1 Answer
Alan P.
Oct 28, 2016

#color(green)(1/(a^2b+1))#

Explanation:

If we temporarily replace #a^2b# with #x#

#(a^2b-1)/(a^4b^2-1) rarr (x-1)/(x^2-1)#

We know that #x^2-1# can be factored as #(x-1)(x+1)#

So #(x-1)/(x^2-1)= cancel(x-1)/((cancel(x-1))(x+1))=1/(x+1)#

Restoring #x# back to #a^2b#, we have
#color(white)("XXX")(a^2b-1)/(a^4b^2-1)= 1/(a^2b+1)#

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