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# ​ Need Help

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2.) Consider the rational expression .

[4x^2-4] /  [x^2 + 4x + 3]

Select true or false for each statement:

4 is a factor of the numerator:

x+1 is a factor of the denominator

the denominator has 2 terms

the numerator has 2 terms

Oct 19, 2018
edited by whosmans  Oct 19, 2018

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\(\dfrac{4x^2-4}{x^2+4x+3} = \dfrac{4(x^2-1)}{(x+3)(x+1)}=\dfrac{4(x+1)(x-1)}{(x+3)(x+1)}\)

True

True

This is a bit tricky.  Clearly there are two terms in both the numerator and denominator as written but we should cancel out the (x+1) term in both the numerator and denominator and obtain

\(\dfrac{4(x-1)}{x+3}\)

This has only a single term in both the numerator and denominator.