Determine whether the following statement makes sense or does not make sense, and explain the reasoning.
When performing the division, 8x/x+3 divided by (x+3)^2/x-6, a student began by dividing the numerator and the denominator by the common factor, x+3
A. The statement does not make sense because. though there seems to be the common factor of x+3, the process is not correct. When dividing rational expressions, the divisor is inverted and the expressions are multiplied. So. the expression becomes 8x/x+3 • x-6/(x+3)^2 and there is no common factor in the numerator and denominator.
B. The statement makes sense because, when dividing rational expressions, the expressions are both inverted and then multiplied. So, the expression becomes x+3/8x • x-6/(x+3)^2 then the common factor between the numerator and denominator is divided out.
C. The statement makes sense because there is a common factor of x+3 when dividing rational expressions, the common factor between the
numerator and denominator is divided out.
D. The statement does not make sense, though there seems to be the common factor of x+3, the process is not correct. When dividing rational expressions, the divisor is inverted and the expressions are multiplied. So, the expression becomes x+3/8x • (x+3)^2/x-6 and there is no common factor in the numerator and denominator.