y^2-4y+3/y^2*4y+12/y^2-2y+1

2y(2y+3)/

I need some help with this problem please I can not seem to work it right.

To simplify the given expression, let's break it down step by step.

1. Start by simplifying each fraction individually:

For the first fraction, y^2 - 4y + 3 / y^2:
This cannot be simplified further since the numerator is a quadratic expression.

For the second fraction, 4y + 12 / y^2 - 2y + 1:
We can factor the denominator as (y - 1)(y - 1) = (y - 1)^2.

2. Rewrite the original expression using the simplified fractions:

(y^2 - 4y + 3 / y^2) * (4y + 12 / (y - 1)^2)

3. Now, look for common factors between the numerator and denominator of each fraction and simplify them:

For the first fraction, we have:
(y - 1)(y - 3) / y^2

For the second fraction, we have:
4(y + 3) / (y - 1)^2

4. Substitute the simplified fractions back into the original expression:

[(y - 1)(y - 3) / y^2] * [4(y + 3) / (y - 1)^2]

5. Simplify further if possible:

Notice that (y - 1) is a common factor between the numerator and denominator. We can cancel it out:

(y - 3) / y^2 * 4(y + 3) / (y - 1)

6. Multiply the remaining terms:

4(y - 3)(y + 3) / y^2(y - 1)

7. Now, we have the simplified form of the expression:

4(y - 3)(y + 3) / y^2(y - 1)

I hope this step-by-step explanation helps you understand how to simplify the given expression. Let me know if you have any further questions!