Question

How do you solve [x*(y-x)]/[y*(x-y)]?

A) Factor the expression.
B) Cross-multiply and simplify.
C) Take the derivative of the expression.
D) Integrate the expression.

Answer 1

To solve the expression [x*(y-x)]/[y*(x-y)], the correct approach is to factor the expression, which simplifies to -x/y after the terms (y-x) and (x-y) cancel out.

Step-by-step explanation:

To solve the expression [x*(y-x)]/[y*(x-y)], the most appropriate method would be to factor the expression. This is because the numerator and the denominator have similar terms that can be factored out, simplifying the expression. In fact, you'll notice that (y-x) is equivalent to -(x-y), which allows for significant simplification:

[x*(y-x)]/[y*(x-y)] = [x*(-(x-y))]/[y*(-(y-x))] = [-x/(y)]

After factoring, the expression simplifies to -x/y, since the terms (y-x) and (x-y) cancel out, leaving us with the simplified ratio of -x to y.