Final answer:
The rational expression (7x²+7x+4x+4)/(7x²+4x-28x-16) simplifies to (7x²+11x+4)/(7x²-24x-16). No further simplification is possible as there are no common factors and the quadratics cannot be factored with the information given.
Step-by-step explanation:
To simplify the rational expression (7x²+7x+4x+4)/(7x²+4x-28x-16), we should first simplify both the numerator and the denominator by combining like terms. The numerator simplifies to 7x² + (7x + 4x) +4, which is equivalent to 7x² + 11x + 4. The denominator can be simplified to 7x² + (4x - 28x) - 16, which simplifies to 7x² - 24x - 16.
At this point, we can check for common factors, but both the numerator and the denominator are quadratic expressions without common factors. Unfortunately, in this case, without further information (like the possibility of factoring these quadratics), we cannot simplify the expression more than we already have. We eliminate terms wherever possible, but here, it doesn't help in simplification.
To check the answer, we can observe that no common terms exist between the numerator and the denominator as simplified, and there is no further simplification possible without additional context or instructions (such as factoring).