Express the following rational expressions in its lowest term.
$\frac{(x - 3) (x^{2} - 5 x + 4)}{(x - 4) (x^{2} - 2 x - 3)}$

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

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

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None of the above

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Solution

The correct option is B $\frac{x - 1}{x + 1}$
$p (x) = (x - 3) (x^{2} - 5 x + 4)$
= $(x - 3) (x - 1) (x - 4)$
$q (x) = (x - 4) (x^{2} - 2 x - 3)$
= $(x - 4) (x - 3) (x + 1)$

Since H.C.F of [p(x),q(x)] is not 1, this is not the lowest terms.
Now $\frac{p (x)}{q (x)} = \frac{(x - 3) (x - 1) (x - 4)}{(x - 4) (x - 3) (x + 1)}$

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

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