Final answer:
To divide rational expressions involving quadratics, we can simplify the expression by multiplying by the reciprocal of the second fraction, factor the quadratic expressions in the numerators and denominators, and cancel out common factors.
Step-by-step explanation:
To divide rational expressions, we can use the rule that states dividing by a fraction is equivalent to multiplying by its reciprocal. In this case, we have the expression (x-2)/(x²+2x-3) divided by (4x-8)/(x²+4x+3). To simplify, we first write the division as multiplication by the reciprocal of the second fraction, which is (x²+4x+3)/(4x-8).
Next, we can factor the quadratic expressions in the numerators and denominators. The first numerator can be factored as (x-2) and the second numerator as (x-1)(x+3). The first denominator can be factored as (x-1)(x+3) and the second denominator as 4(x-2).
Cancelling out common factors, we are left with (x-2)(x+3)/4. This is the simplified form of the given expression.