Question

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

Answer 1

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.

Answer 2

The mistake done is in multiplying the numerator values after Taking LCM.

Correct answer is $\frac{3}{(x-2)(x+1)}$

Step-by-step explanation:

We will first solve the expression and then identify the error.

$\frac{1}{x-2}-\frac{1}{x+1}$

Solving:

$\frac{1}{x-2}-\frac{1}{x+1}$

Finding LCM of (x-2) and (x+1) we get (x-2)(x+1)

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

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

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

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

So, the mistake done is in multiplying the numerator values after Taking LCM. x+1-(x-2) we get x+1-x+2 because (-)*(-) = + and (-)*(+)= -. So, we get

x-x+1+2 we know that x-x=0 and 1+2=3

So, correct answer is $\frac{3}{(x-2)(x+1)}$

Keywords: Rational Expressions

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