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

1 Answer
Oct 8, 2015

Answer:

#(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)#