Final answer:
The given expression (18x²-12x) / (63x) simplifies to (2x-1)/7 when factoring and canceling common terms, making the correct answer (a).
Step-by-step explanation:
To simplify the expression (18x²-12x) / (63x), we should factor and cancel out any common factors in the numerator and denominator. Starting with the numerator: 18x² can be factored into 6 * 3x², and -12x can be factored into 6 * -2x. Thus, the numerator becomes 6x(3x-2).
Looking at the denominator, 63x can be broken down into 9 * 7x. To simplify the fraction, we can divide both the numerator and denominator by the common factor of 9x, leaving us with:
(6x/9x)*(3x-2)/7 = (2x-1)/7.