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!