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

Answer 1

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

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)#

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Answer 2

Julia Adams

To simplify the expression (2x^2+11x+5)/(3x^2+17x+10), you can factorize the numerator and denominator and then cancel out any common factors. The factored form of the numerator is (2x+1)(x+5), and the factored form of the denominator is (3x+2)(x+5). By canceling out the common factor (x+5), the simplified form of the expression is (2x+1)/(3x+2).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.