[2y^2+11y+5]/[4y^2+4y+1] / [2y^3+10y^2]/[4y^3]
=2y over (2y+1), right?
is this how you did it?
2Y^2+11Y+5/4Y^2+4Y+1 / 2Y^3+10Y^2= (Y+5)(Y+1)/(Y+1)(Y+1) / 2Y^2(Y+5)/4Y^3= 1/Y+1 / 4Y^3/2Y^2= 2Y OVER Y+1
You didn't believe me ?
http://www.jiskha.com/display.cgi?id=1253821138
To simplify the expression [2y^2+11y+5]/[4y^2+4y+1] / [2y^3+10y^2]/[4y^3], we need to follow a few steps:
Step 1: Find the reciprocal of the second fraction in the numerator and denominator.
So, the reciprocal of [2y^3+10y^2]/[4y^3] is [4y^3]/[2y^3+10y^2].
Step 2: Rewrite the expression with the complex fraction divided by its reciprocal.
The expression becomes [2y^2+11y+5]/[4y^2+4y+1] * [4y^3]/[2y^3+10y^2].
Step 3: Factor out any common terms in the numerator and denominator.
In the first fraction, we can factorize the numerator as (2y + 1)(y + 5) and the denominator as (2y + 1)(2y + 1), which can be simplified further as (2y + 1)^2.
In the second fraction, we can factorize the common factor of 2y^2 from the numerator and denominator, resulting in (2y^2)(2y + 5) / (y^2 + 5y).
Now, the expression becomes [(2y + 1)(y + 5)] / [(2y + 1)^2] * [(2y^2)(2y + 5)] / (y^2 + 5y).
Step 4: Cancel out any common factors that appear in both the numerator and denominator.
In this case, (2y + 1) is a common factor in the numerator and denominator, so we can cancel them out. Additionally, (2y^2) is a common factor in the numerator and denominator that can also be canceled out.
After canceling out the common factors, the expression simplifies to [y + 5] / [2y + 1] * [2y + 5] / (y^2 + 5y).
Step 5: Simplify further if possible.
Since there are no more common factors to cancel out or simplify, we can leave the expression as it is.
Therefore, the simplified expression is [y + 5] / [2y + 1] * [2y + 5] / (y^2 + 5y).
Note that it does not reduce to 2y / (2y + 1).