Question

Describe the error made in subtracting the two rational expressions shown:

Answer 1

The correct answer is:

The numerator of the answer should be 3.

Explanation:

The common denominator has been found accurately and the expressions have been accurately changed to reflect that denominator.

The mistake occurs when the subtraction is done.  The subtraction of the numerators would be

(x+1)-(x-2)

Distributing the subtraction sign would give us

x+1-x--2 = x+1-x+2

The x's would cancel, leaving 1+2 = 3.

Answer 2

These are the answers on E2020!

You must subtract all terms of the numerator being subtracted out, not just the first term.  The negative 2 should have been subtracted out to get a numerator of x + 1 - x + 2.  The simplified numerator of the difference should be 3, not –1.