Y^2-4y+3/y^2-9*4y+12/y2-2y+1=
16y^4+36/2y^5+8
check this please
oh my
(y^2 - 4y + 3)/(y^2 - 9) * (4y + 12)/(y^2 - 2y + 1)
= (y-3)(y-1)/[(y+3)(y-3)] * 4(y+3)/[(y-1)(y-1)]
= 4/(y-1) y ≠ ±1, ±3
To simplify the given expression:
1. Let's factor each expression separately:
a) Factor the numerator of the first fraction, Y^2 - 4y + 3:
Y^2 - 4y + 3 = (Y - 3)(Y - 1)
b) Factor the denominator of the first fraction, Y^2 - 9:
Y^2 - 9 = (Y - 3)(Y + 3)
c) Factor the numerator of the second fraction, 4y:
4y = 4 * y
d) Factor the denominator of the second fraction, Y^2 - 2y + 1:
Y^2 - 2y + 1 = (Y - 1)(Y - 1) = (Y - 1)^2
2. Now, rewrite the expression with the factored forms:
((Y - 3)(Y - 1) / (Y - 3)(Y + 3)) * (4 * y / (Y - 1)^2)
3. Simplify the expression by canceling out common factors:
(Y - 1) cancels out from the numerator of the first fraction and the denominator of the second fraction:
(Y - 1) / (Y + 3) * (4 * y / (Y - 1))
4. Simplifying further by canceling out common factors:
(Y - 1) cancels out completely:
4y / (Y + 3)
5. The simplified expression is 4y / (Y + 3).
Now, let's check if this is equal to 16y^4 + 36 / (2y^5 + 8):
If we substitute y = 0 into both expressions, we get:
- 4y / (Y + 3) = 0 / (0 + 3) = 0
16y^4 + 36 / (2y^5 + 8) = 16(0)^4 + 36 / (2(0)^5 + 8) = 36 / 8 = 4.5
Since 0 is not equal to 4.5, the given expression:
16y^4 + 36 / (2y^5 + 8)
is not equivalent to the simplified expression:
4y / (Y + 3).