To solve this problem, we must determine which of the given expressions is equivalent to the original one. The given expressions are:
(1) (x - 10) * (x + 3) / ((x - 7) * (x + 3))
(2) (x + 3) * (x - 10) / ((x + 3) * (x - 7))
(3) (x - 10) / (x - 7)
The first step is to factorize the given expression. The expression (x²-7x-30)/(x²-4x-21) can be handwritten as
(x - 10)(x + 3) / (x - 7)(x + 3).
Now, let's move to the west terms.
1. The 1st expression is (x - 10) * (x + 3) / ((x - 7) * (x + 3)). If you look closely, this expression is identical to the factorized form of the original expression. So, this could be the right answer.
2. The 2nd expression is (x + 3) * (x - 10) / ((x + 3) * (x - 7)). This expression is essentially the same as the first west term, except the order of the terms is different. However, in math, the order in which we multiply doesn't matter, so technically this expression is also equal to the original. But traditionally, we write terms in a decreasing order of their powers(X's are before the constants). Hence, this expression isn't considered here.
3. The 3rd expression is (x - 10) / (x - 7). Clearly, we can see that the denominator is missing a term that the original expression has ( (x+3) ), which makes it different from the other expressions and hence, it isn't equivalent to the original expression.
So, by narrowing down the possibilities, we find that the 1st expression is the equivalent rational expression to the original one in the west terms.