Question

Mr. Knotts found the difference of the following expression. Which statement is true about Mr. Knotts’s work?

StartFraction x Over x squared minus 1 EndFraction minus StartFraction 1 Over x minus 1 EndFraction

Step 1: StartFraction x Over (x + 1) (x minus 1) EndFraction minus StartFraction 1 Over x minus 1 EndFraction

Step 2: StartFraction x Over (x + 1) (x minus 1) EndFraction minus StartFraction 1 (x + 1) Over (x + 1) (x minus 1) EndFraction

Step 3: StartFraction x minus x + 1 Over (x + 1) (x minus 1) EndFraction

Step 4: StartFraction 1 Over (x + 1) (x minus 1) EndFraction
In step 1, he did not correctly factor the denominator.
In step 2, he did not use the correct common denominator.
In step 3, he did not distribute the negative sign when he subtracted.
In step 4, he did not correctly subtract the numerator.

Answer 1

Answer:

He did not distribute the negative sign when he subtracted.

Step-by-step explanation:

x-(x+1) is equal to a -1. He did not distribute the negative.

Answer 2

In third step, he did not distribute the negative sign when he subtracted. Then the correct option is C.

What is Algebra?

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

Mr. Knotts found the difference of the following expression.

The expression is given below.

$\rm \rightarrow \dfrac{x}{x^2-1} - \dfrac{1}{x -1}$

Then the first step of the expression will be

$\rm \rightarrow \dfrac{x}{(x+1)(x-1)} - \dfrac{1}{x -1}$

The second step of the expression will be

$\rm \rightarrow \dfrac{x}{(x+1)(x-1)} - \dfrac{1(x+1)}{(x+1)(x -1)}$

The third step of the expression will be

$\rm \rightarrow \dfrac{x - (x +1)}{(x+1)(x-1)}\\\\\rm \rightarrow \dfrac{x - x -1}{(x+1)(x-1)}$

In third step, he did not distribute the negative sign when he subtracted.

Then the correct option is C.

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