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(4y^2-9)/(2y^2+y-3) always fully factor everything when you're simplifying! Top is a difference of squares expression, bottom you can simplify by factoring. TOP: (?y-?)(?y+?) First ? of each bracket is square root of first coefficient (4) Second? of each bracket is square root of second coefficient (9): (2y-3)(2y+3) BOTTOM: (2y^2 +y -3) 3 is negative, therefore one bracket is positive, the other is negative (?y-?)(?y+?) First ? of each bracket will be factors of first coefficient (2) Second ? of each bracket will be factors of last coefficinet (3) Mix and match until upon multiplying it out, you can get the middle term; 1y; (2y-3)(y+1) 2y^2 -3 -3y +2y 2y^2 -1y -3 Not quite, so let's switch the signs around: (2y+3)(y-1) 2y^2 -3 +3y -2y 2y^2 +y -3 Perfect, so our bottom is going to be: (2y+3)(y-1) SO NOW WE"VE SIMPLIFIED (4y^2-9)/(2y^2+y-3) INTO (2y+3)(2y-3)/(2y+3)(y-1) NOTE that the (2y+3)s cancel each other out, leaving you with 1(2y-3)/1(y-1) (2y-3)/(y-1) can't factor/simplify further, so this is the final answer. So it's going to be other option 2 or 4. TO FIND RESTRICTIONS, set each part containing 'y' IN ALL DENOMINATORS WE'VE ENCOUNTERED SO FAR equal to 0. The reason for this; anything multiplied by zero in the denominator makes the equation UNDEFINED, so we need to find out what those values are by setting them equal to 0 denominators we've come across: (2y+3) and (y-1) (2y+3)=0 and (y-1)=0 2y= -3 and y= 1 y= -3/2 and y= 1 THEREFORE the restrictions we have our y= cannot equal -3/2, 1, THEREFORE THE SECOND OPTION IS CORRECT
so wait whats the answer ? and the restrictions ? @abayomi12