Question

Describe the error made in subtracting the two rational expressions shown

Answer 1

Answer:

The minus sign between the two fractions was not distributed correctly.

Step-by-step explanation:

The error made in this solution of rational fractions' subtraction is that the minus sign between the two terms will change the signs of numerator of second fraction so the numerator in the answer will be 3.

The correct solution is:

$\frac{1}{x-2} - \frac{1}{x+1}\\=\frac{x+1}{(x-2)(x+1)} - \frac{x-2}{(x-2)(x+1)}\\=\frac{x+1-(x-2)}{(x+1)(x-2)}\\=\frac{x+1-x+2}{(x+1)(x-2)}\\=\frac{3}{(x+1)(x-2)}$

Hence,

The error was in the last step of subtraction.

Answer 2

Answer:

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.

Step-by-step explanation:

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