Question

Which of the following is the simplified form of 4y2-1/2y2+3-2

Answer 1

(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

Answer 2

so wait whats the answer ? and the restrictions ? @abayomi12