Question

How do I find the error in the rational expression?

Answer 1

`\stackrel{\textit{not distributed yet}}{\cfrac{x+1}{(x-2)(x+1)}\stackrel{\downarrow }{\text{\LARGE -}}\cfrac{x-2}{(x-2)(x+1)}}\implies \stackrel{\textit{already distributed}}{\cfrac{x+1}{(x-2)(x+1)}\stackrel{\downarrow }{\text{\LARGE +}}\cfrac{-x+2}{(x-2)(x+1)}} \\\\\\ \cfrac{x+1-x+2}{(x-2)(x+1)}\implies \cfrac{3}{(x-2)(x+1)}`

Answer 2

The error is in the 3rd step. The denominator should be 3, not -1.

Explanation:

The third step has an error. The second fraction is subtracted from the first. The calculation should have been (x+1) - (x-2). x+1-x+2 = 3.

See the attached worksheet.