Question

Which expression is equivalent to (x - a) / (x - b) * (x - c)?

A) x(-a - b + c)
B) x(a + b - c)
C) x(a - b + c)
D) x(-a + b + c)

Answer 1

After multiplying and simplifying the expression (x - a) / (x - b) * (x - c), none of the options A, B, C, or D are directly equivalent to the original expression without additional information.

Step-by-step explanation:

The expression (x - a) / (x - b) * (x - c) can be simplified by performing the multiplication first.

Let's multiply (x - c) by the numerator (x - a):

(x - a)(x - c) = x^2 - cx - ax + ac

Now we simplify this expression:

x(x - c - a + ac/b)

Since there is a division by (x - b), it's equivalent to multiplying the term by 1/(x - b), which means multiplying each term in the binomial (x - c - a + ac/b) by 1/(x - b).

After both multiplication and simplification, none of the provided options A, B, C, or D are equivalent to the original expression, as the term ac/b cannot be distributed over x without additional information.