Multiply. Show all restictions of the answer. Show your work.

2x^2+7x+3/4x^2-1 * 2x^2+x-1/x^2+2x-3

1 answer

To multiply the given expressions, we need to multiply the numerators and the denominators separately and then simplify the resulting expression.

Numerator:
(2x^2 + 7x + 3) * (2x^2 + x - 1)
= 4x^4 + 2x^3 - 2x^2 + 7x^3 + 3x^2 - 3x + 3x^2 + x - 1
= 4x^4 + 9x^3 + 6x^2 - 4x - 1

Denominator:
(4x^2 - 1) * (x^2 + 2x - 3)
= (2x + 1)(2x - 1)(x + 3)(x - 1)
= (4x^2 - 1)(x^2 + 2x - 3)
= 4x^4 + 8x^3 - 12x^2 - x^2 - 2x + 3

Final answer:
(4x^4 + 9x^3 + 6x^2 - 4x - 1) / (4x^4 + 8x^3 - 12x^2 - x^2 - 2x + 3)

The restrictions of the answer are the values of x that makes the denominator equal to zero. So, we set the denominator equal to zero and solve for x:

4x^4 + 8x^3 - 12x^2 - x^2 - 2x + 3 = 0

Simplifying the equation, we have:
4x^4 + 8x^3 - 13x^2 - 2x + 3 = 0

Unfortunately, finding the exact values of x that satisfy this equation may require numerical methods or factoring techniques.

Therefore, the restrictions of the answer cannot be determined without further information or additional calculations.