Question

Which expression is equivalent to (x + 3)/(x^2 - 2x - 3) divided by (x^2 + 2x - 3)/(x - 1) if no denominator equals zero?

a) 1/(x^2 - 2x - 3)
b) 1/(x^2 - 4x + 3)
c) 1/(x^2 + 3x - 3)
d) (x + 3)/(x - 1)

Answer 1

The equivalent expression to (x + 3)/(x^2 - 2x - 3) divided by (x^2 + 2x - 3)/(x - 1) is 1/(x^2 - 2x - 3), which corresponds to option a) after factoring the denominators and canceling out common terms.

Step-by-step explanation:

The question asks which expression is equivalent to (x + 3)/(x2 - 2x - 3) divided by (x2 + 2x - 3)/(x - 1) given that no denominator equals zero. To solve this, we need to treat the division of two fractions as multiplication by the reciprocal of the second fraction.

Step 1: Write the division as multiplication by the reciprocal.
((x + 3)/(x2 - 2x - 3)) × ((x - 1)/(x2 + 2x - 3))

Step 2: Factor the denominators to simplify.
((x + 3)/((x - 3)(x + 1))) × ((x - 1)/((x + 3)(x - 1)))

Step 3: Cancel out common terms in the numerator and denominator.
The (x + 3) and (x - 1) terms cancel out, leaving us with:

1/(x - 3)(x + 1), which is equivalent to 1/(x2 - 2x - 3).

Thus, the correct answer is option a) 1/(x2 - 2x - 3).