Final answer:
The simplification of the expression (1/4x + 1/3) + (1/7x - 3/8) results in (3x + 19)/(28x), corresponding to option d.
Step-by-step explanation:
The simplification of the algebraic expression (1/4x + 1/3) + (1/7x - 3/8) is achieved by combining like terms and finding a common denominator.
To do this, first combine the terms with an 'x' and the constant terms separately. For the 'x' terms, the common denominator is 28x, so you would get Result:x terms = ((1×4)+(1×3)) / (4×7)x = (7+4)/(28x) = 11/(28x). For the constants: Result:constant terms = (8×3 + 3×4) / (3×8) = (24-9) / 24 = 15 / 24, which simplifies to 5/8 when divided by 3. To combine these results, you would add 11/(28x) to 5/8, which requires a common denominator of 28x. This means converting 5/8 to a fraction over 28x, which is (5×35) / (8×35) = 175/(28x).
Adding these together gives you (11 + 175) / (28x) = 186/(28x), which simplifies to (3x + 19)/(28x) after canceling out common factors. Therefore, the correct answer is option d.