Question

How do you simplify `(2x^2+11x+5)/(3x^2+17x+10)`?

Answer 1

`(2x + 1)/(3x + 2)`

Explanation:

Factor the numerator `y1 = 2x^2 + 11x + 5 =` 2(x + p)(x + q)
Use new AC Method to factor trinomials.
Converted trinomial: `x^2 + 11x + 10.`
Factor pairs of 10 --> (1, 10). This sum is 11 = b. Then `p = 1/2` and `q = 10/2 = 5`.
`y1 = 2(x + 1/2)(x + 5) = (2x + 1)(x + 5)`

Next, factor the denominator:
`y2 = 3x^2 + 17x + 10.`
Converted trinomial: `x^2 + 17x + 30.`
Factor pairs of (30) --> (2, 15). This sum is 17 = b. Then `p = 2/3` and `q = 15/3 = 5.`
`y2 = 3(x + 2/3)(x + 5) = (3x + 2)(x + 5)`.
Finally: `(y1)/(y2) = [(2x + 1)(x + 5)]/[(3x + 2)(x + 5)] = (2x + 1)/(3x + 2)`