Question

What mistake did he make?

A) He excluded x=1, which only makes the numerator of the divisor equal to zero

B) He excluded x=-1, which doesn’t make the denominator in the final quotient equal to zero

C) He didn’t rewrite the dividend correctly

D) He didn’t rewrite the divisor correctly

Answer 1

C) He didn't write the dividend correctly.

Explanation:

The mistake that someone made while executing the division:

`(-x+1)/(3x-6)/(x^2-1)/(x+4)`

was incorrectly rewriting the dividend.

The dividend's numerator:

`-x + 1`

should have been rewritten as:

`-(x-1)` ✅

Instead, a -1 was incorrectly factored out without accounting for the second term (+1):

`-(x+1)` ❌

When we expand this incorrectly factored expression, we get:

`-x-1`,

which is NOT what the dividend originally had as its numerator.