Question

What is the GCF of the numerator & denominator below? (x-2)(x+3)/x^2+4x+3

Answer 1

Answer:

Step-by-step explanation:

Factorize the denominator

Sum = 4

Product = 3

Factors = 1 , 3    {1*3 = 3 and  1+3 = 4}

x² + 4x + 3 = x² + x    + 3x + 1*3

                 = x(x + 1) + 3(x + 1)

                 = (x + 1)(x + 3)

GCF of the numerator and denominator = (x + 3)

Answer 2

Answer:

GCD of given expressions is (x+3)

Step-by-step explanation:

let's simply the denominator : -

=》

${x}^{2} + 4x + 3$

=》

$x {}^{2} + 3x + x + 3$

=》

$x(x + 3) + 1(x + 3)$

=》

$(x + 1)(x + 3)$

so, by plugging (x + 1) (x + 3) in denominator,

=》

$\frac{(x - 2)(x + 3)}{(x + 1)(x + 3)}$

and here, we can see that the only common factor in both numerator and denominator is

(x + 3)

so, GCD = (x + 3)