Question 218262
Please simplify:

{{{4x^2 + 4x + 1/(1-4x^2)}}}


Step 1. Multiply by {{{(1-4x^2)/(1-4x^2)=1}}} to put expression in a common denominator


{{{((1-4x^2)*(4x^2+4x)+1)/(1-4x^2)}}}={{{((4x+4x^2)(1-4x^2)+1)/(1-4x^2)}}}


Step 2. Use FOIL method to multiply out the terms.


{{{(4x-16x^3+4x^2-16x^4+1)/(1-4x^2)}}}


Step 3.  Arrange numerator and denominator in descending order


{{{(-16x^4-16x^3+4x^2+4x+1)/(-4x^2+1)}}}


Step 4.  ANSWER is {{{4x^2 + 4x + 1 /(1-4x^2)=(-16x^4-16x^3+4x^2+4x+1)/(-4x^2+1)}}}


I hope the above steps were helpful.


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And good luck in your studies!


Respectfully,
Dr J