Final answer:
The simplified exchange rate Salma will receive can be found by multiplying the expression for dollars (12x²+15x-18)/(2x²+14x+20) by the reciprocal of the expression for euros (2x²-x-3)/(x²+6x+5), and then factoring and simplifying the resulting expression.
Step-by-step explanation:
The question involves finding the simplified exchange rate that Salma will receive for her dollars per euro. To find this rate, we must multiply the expression for the number of dollars by the reciprocal of the expression for the number of euros. The expression for dollars is (12x²+15x-18)/(2x²+14x+20) and the expression for euros is (2x²-x-3)/(x²+6x+5). Multiplying the dollars expression by the reciprocal of the euro expression gives us the exchange rate in dollars per euro.
To simplify these expressions, we should first factor both the numerators and the denominators to see if any common factors can be canceled out. This will give us the simplest form of the exchange rate. It is important to note that, at this point, we are assuming Salma has not given a specific value for 'x', so we are keeping the expressions in terms of 'x'. However, if Salma provided a specific value for 'x', then we would substitute that value in to get the exact exchange rate.
Given the complexity of the expressions, this task involves skills in algebraic manipulation, particularly in factoring quadratic equations and simplifying rational expressions, which are commonly taught in high school mathematics courses.