find the reciprocal  6y2+4y

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I'm assuming this is 6y^2 + 4y.  Factor out 2y from both terms.  2y (3y +2).   Write one (1) as a numerator and the rest as a denominator. 1 / [(2y)(3y +2)]     That is the reciprocal of your starting number and its factored. w/o factoring its just : 1 / (6y^2 + 4y)