X+3/3x+6 multiply x^2+4x-2/x^2+4x+3

Answer 1

To multiply two fractions, you simply multiply their numerators together and their denominators together.

So, for the expression (x + 3)/(3x + 6) multiplied by (x^2 + 4x - 2)/(x^2 + 4x + 3), we have:

((x + 3)(x^2 + 4x - 2))/((3x + 6)(x^2 + 4x + 3))

Now, we can simplify each of the factors.

The numerator can be expanded as follows:
(x + 3)(x^2 + 4x - 2) = x(x^2 + 4x - 2) + 3(x^2 + 4x - 2) = x^3 + 4x^2 - 2x + 3x^2 + 12x - 6 = x^3 + 7x^2 + 10x - 6

The denominator can also be expanded:
(3x + 6)(x^2 + 4x + 3) = 3x(x^2 + 4x + 3) + 6(x^2 + 4x + 3) = 3x^3 + 12x^2 + 9x + 6x^2 + 24x + 18 = 3x^3 + 18x^2 + 33x + 18

So, the final expression is given by:
(x^3 + 7x^2 + 10x - 6)/(3x^3 + 18x^2 + 33x + 18)