Final answer:
The division of the given complex fractions simplifies to (x+3)/(x+1) by multiplying the first fraction by the reciprocal of the second fraction and canceling out terms, resulting in option d.
Step-by-step explanation:
The student has been asked to find an expression equivalent to the division of two complex fractions: (x+3)/(x²-2x-3) divided by (x²+2x-3)/(x+1). To solve this, we need to multiply the first fraction by the reciprocal of the second one.
Firstly, we will find the reciprocal of the second fraction, which is (x+1)/(x²+2x-3).
Now we multiply the first fraction by this reciprocal: ((x+3)/(x²-2x-3)) × ((x+1)/(x²+2x-3)).
Upon closer inspection, we notice that the numerator of the first fraction is the factor of the denominator of the second fraction and vice versa. So when we multiply the two fractions, the numerators and denominators cancel out respectively, leaving us with (x+3)/(x+1), which is the simplified equivalent expression. Hence, the correct answer is d. (x+3)/(x+1).