Question

Сократи дробь 3x^2 + 7x - 6 и найдите значение при x=3 __________ x^2 - x - 12

Answer 1

3x^2+7x-6=3x^2+9x-2x-6=3x*(x+3)-2(x+3)   =     (x+3) * (3x-2)
Подставляем x= (3+3)*(3*3-2)= 9*7=   63

x^2-x-12= x^2+3x-4x-12=x*(x+3)-4*(x+3)    =     (x+3)*(x-4)
Подставляем х= (3+3)*(3-4)=9*(-1) =  -9

Ответь мой ответ лучшим, пожалуйста =)

Answer 2

To simplify the fraction, we can factor the numerator and the denominator and then cancel out any common factors. Let's start with the numerator:

Numerator: 3x^2 + 7x - 6

To factor the numerator, we look for two numbers whose product is equal to the product of the leading coefficient (3) and the constant term (-6) and whose sum is equal to the coefficient of the middle term (7). The two numbers are 9 and -2.

So, we can write the numerator as:

Numerator: 3x^2 + 7x - 6 = 3x^2 + 9x - 2x - 6

Now, we can group the terms and factor them:

Numerator: 3x^2 + 9x - 2x - 6 = 3x(x + 3) - 2(x + 3)

Now, we can factor out the common factor (x + 3):

Numerator: 3x(x + 3) - 2(x + 3) = (3x - 2)(x + 3)

Next, let's factor the denominator:

Denominator: x^2 - x - 12

To factor the denominator, we look for two numbers whose product is equal to the product of the leading coefficient (1) and the constant term (-12) and whose sum is equal to the coefficient of the middle term (-1). The two numbers are -4 and 3.

So, we can write the denominator as:

Denominator: x^2 - x - 12 = x^2 - 4x + 3x - 12

Now, we can group the terms and factor them:

Denominator: x^2 - 4x + 3x - 12 = x(x - 4) + 3(x - 4)

Now, we can factor out the common factor (x - 4):

Denominator: x(x - 4) + 3(x - 4) = (x + 3)(x - 4)

Now, the fraction becomes:

(3x^2 + 7x - 6) / (x^2 - x - 12) = (3x - 2)(x + 3) / (x + 3)(x - 4)

Notice that (x + 3) appears in both the numerator and denominator, so we can cancel them out:

(3x^2 + 7x - 6) / (x^2 - x - 12) = (3x - 2) / (x - 4)

Now, to find the value when x = 3, we substitute x = 3 into the simplified expression:

(3x - 2) / (x - 4) = (3 * 3 - 2) / (3 - 4) = (9 - 2) / (-1) = 7 / -1 = -7

So, when x = 3, the value of the expression is -7.