Question

Сократите дробь 3x^2+7x-6/x2-9 при x не = +- 3

Answer 1

(3х²+7х-6)/(х²-9)=
3х²+7х-6=0
Д=7²+72=49+72=121=11²
х=(-7±11)/6
х1=-3;х2=4/6=2/3
=3(х+3)(х-2/3)/(х-3)(х+3)=3(х-2/3)/(х-3)=
(3х-2)/(х-3)

Answer 2

To simplify the fraction (3x^2 + 7x - 6) / (x^2 - 9) while excluding the values of x when x = ±3, we need to factor both the numerator and the denominator and then cancel out the common factors.

1. Factor the numerator and denominator:

Numerator: 3x^2 + 7x - 6 This can be factored as (3x - 2)(x + 3).

Denominator: x^2 - 9 This is a difference of squares and can be factored as (x + 3)(x - 3).

2. Cancel out the common factor (x + 3) from the numerator and denominator:

(3x^2 + 7x - 6) / (x^2 - 9) = [(3x - 2)(x + 3)] / [(x + 3)(x - 3)]

3. Simplify the expression:

Now, since we are excluding x = ±3, we can cancel out the common factor (x + 3):

(3x^2 + 7x - 6) / (x^2 - 9) = (3x - 2) / (x - 3)

So the simplified fraction, excluding x = ±3, is (3x - 2) / (x - 3).