Home > Algebra > Division of Rational Expressions

How do you factor #(7x^2+11x-6)/(x^2-4)#?

Answer 1

#(7x - 3)/(x - 2)#

First, factor the numerator y by the new AC Method (Socratic Search). y = 7x^2 + 11x - 6 = 7(x + p)(x + q) Converted trinomial y' = x^2 + 11x - 42 = (x + p')(x + q') p' and q' have opposite signs. Factor pairs of (ac = -42) --> (-2, 21(-3, 14). This last sum is (11 = b). Then p' = -3 and q' = 14. Back to original trinomial y, #p = p'/a = -3/7#, and #q = (q')/a = 14/7 = 2.# Factor form of y: y = 7(x - 3/7)(x + 2) = (7x - 3)(x + 2)# Factored form of #f(x) = ((7x - 3)(x + 2))/((x - 2)(x + 2)) =# #f(x) = (7x - 3)/(x - 2)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Jameson Allen

To factor the expression (7x^2+11x-6)/(x^2-4), we can first factor the numerator and denominator separately.

The numerator, 7x^2+11x-6, can be factored as (7x-2)(x+3).

The denominator, x^2-4, is a difference of squares and can be factored as (x-2)(x+2).

Therefore, the expression can be simplified as (7x-2)(x+3)/((x-2)(x+2)).

By signing up, you agree to our Terms of Service and Privacy Policy

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.