Question

Describe the error made in subtracting the two rational expressions shown: 1/x-2 - 1/x 1 = x 1/(x-2)(x 1)-x-2/(x-2)(x 1) =-1/(x-2)(x 1)

Answer 1

The error made in subtracting the two rational expressions is that the numerator of the first expression is not being multiplied by -1. In order to subtract rational expressions, you need to have a common denominator.

Step-by-step explanation:

The error made in subtracting the two rational expressions is that the numerator of the first expression is not being multiplied by -1. In order to subtract rational expressions, you need to have a common denominator. You should multiply the numerator of the first expression by -1 before subtracting.

So the correct subtraction would be:

(1/x-2) - (1/x)

= (-1/x-2) - (1/x)

= (-1 - x-2)/(x(x-2))

= (-1 - (1/x))/((x-2)(x))

= (-1 - 1)/(x(x-2))

= -2/(x(x-2))