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Question
Difficulty Level:

Easy

MCQ

Aoi tried to reduce the following expression to lowest terms:

3x+3x21\frac{3 x+3}{x^{2}-1}

This is her work:

Factoring the numerator: 3x+3=3(x+1)3 {x}+3=3({x}+1)

Factoring the denominator: x21=(x+1)(x1)x^{2}-1=({x}+1)({x}-1)

Finding excluded values: : x0x \neq 0 and x±3x \neq \pm 3

Reducing to lowest terms:

3x+3x21=3(x+1)(x+1)(x1)=3x+1\frac{3 x+3}{x^{2}-1}=\frac{3(x+1)}{(x+1)(x-1)}=\frac{3}{x+1}

What mistake did Aoi make?

Select all that apply :

She excluded x=0x=0, which doesnot make the denominator equal to 0 .

She excluded x=1x=1, which doesnot make the numerator equal to zero.

She excluded x=1x=-1 whick doesnot make, the new expression equal to 20 .

She did not factor the denominator correctly.

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