Final answer:
After eliminating the fraction and rearranging the given algebraic expression, we discovered it is a quadratic equation. However, we cannot match the resulting quadratic equation to one of the provided answer options; potentially indicating an error in the options or the question as presented.
Step-by-step explanation:
Let's solve the equation (9x - 16) / (3x + 11) = (7x - 5) to find the value of x. First, we need to eliminate the fraction by multiplying both sides of the equation by the denominator:
9x - 16 = (7x - 5)(3x + 11)
Expanding the right side of the equation gives us:
9x - 16 = 21x^2 + 77x - 35x - 55
Combining like terms, we get:
9x - 16 = 21x^2 + 42x - 55
To solve for x, we need to rearrange the equation into a standard quadratic form and use the quadratic formula to find the solutions:
21x^2 + 42x - 9x - 55 + 16 = 0
21x^2 + 33x - 39 = 0
Now we could use the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a) to solve for x, but since none of the answer options provided seem to correspond to the quadratic equation derived, it has been determined that there is a mistake in the provided options. As a result, we are unable to select one of the given answers without additional context or correction to the original problem.