[2y^2+11y+5]/[4y^2+4y+1] / [2y^3+10y^2]/[4y^3]
Would the right answer be 4y^3 over 2y+1?
I got 2y/(2y+1) , y not equal to -1/2,-5,0
4x+2+2x+x2+x
To simplify the expression [(2y^2+11y+5)/(4y^2+4y+1)] / [(2y^3+10y^2)/(4y^3)], you can follow these steps:
1. Divide the numerators and denominators separately.
- Divide the numerator of the first fraction, which is (2y^2+11y+5), by the numerator of the second fraction, which is (2y^3+10y^2).
- Divide the denominator of the first fraction, which is (4y^2+4y+1), by the denominator of the second fraction, which is (4y^3).
2. Simplify each division.
- For the numerator, divide each term of (2y^2+11y+5) by (2y^3+10y^2).
- For the denominator, divide each term of (4y^2+4y+1) by (4y^3).
Let's simplify each division and combine the fractions:
Numerator division:
(2y^2+11y+5)/(2y^3+10y^2)
Both numerator and denominator don't share any common factors, so we cannot simplify this division any further.
Denominator division:
(4y^2+4y+1)/(4y^3)
Both numerator and denominator share a common factor of 1, so we can factor out '1' from both terms.
(1 * 4y^2 + 1 * 4y + 1)/(4y*3)
Simplifying, we get:
(4y^2 + 4y + 1)/(4y^3)
Now, dividing the fractions:
[(2y^2+11y+5)/(2y^3+10y^2)] / [(4y^2+4y+1)/(4y^3)]
To divide one fraction by another, we multiply the first fraction by the reciprocal of the second fraction:
[(2y^2+11y+5)/(2y^3+10y^2)] * [(4y^3)/(4y^2+4y+1)]
Now, multiply the numerators together and the denominators together:
(2y^2+11y+5) * (4y^3) / (2y^3+10y^2) * (4y^2+4y+1)
Expanding the products:
8y^5 + 44y^4 + 20y^3 / 8y^5 + 40y^4 + 8y^3 + 4y^4 + 20y^3 + 4y^2 + 2y + y^3
Combining like terms:
8y^5 + 44y^4 + 20y^3 / 8y^5 + 45y^4 + 21y^3 + 4y^2 + 2y
So, the simplified expression is (8y^5 + 44y^4 + 20y^3) / (8y^5 + 45y^4 + 21y^3 + 4y^2 + 2y).