Final answer:
To solve the expression (34/8−16/3)−14/9, simplify the expression inside the parentheses, subtract the fraction outside the parentheses, find the common denominator, and subtract the fractions.
Step-by-step explanation:
To find the answer to the expression (34/8−16/3)−14/9, we must first simplify within the parentheses. We begin by finding a common denominator for the fractions inside the parentheses, which is 24. The fraction 34/8 converts to 3*34/3*8 = 102/24, and the fraction 16/3 converts to 8*16/8*3 = 128/24.
Now, subtracting the second fraction from the first gives us 102/24 - 128/24 = -26/24. Simplifying -26/24 gives us -13/12. Finally, subtracting 14/9 from -13/12 requires a common denominator, which is 36. We convert -13/12 to -3*13/3*12 = -39/36 and convert 14/9 to 4*14/4*9 = 56/36.
When we subtract, we get -39/36 - 56/36 = -95/36. This fraction cannot be simplified further, so it is our final answer. Therefore, the choices provided (a) 2/3, (b) 5/6, (c) 3/4, and (d) 7/8 are all incorrect.