Find the vertical and horizontal asympotote for (×-2) (×+3)/ (2×+2)

1 answer:

6 0

$\bf \cfrac{(x-2)(x+3)}{2x+2}\implies \cfrac{x^2+x-6}{2x+2}~~ \begin{array}{llll} \leftarrow \textit{2nd degree polynomial}\\ \leftarrow \textit{1st degree polynomial} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{vertical asymptote}}{2x+2=0}\implies 2x=-2\implies x=-\cfrac{2}{2}\implies x=-1$

when the degree of the numerator is greater than the denominator's, then it has no horizontal asymptotes.

quick note:

when the degree of the numerator is 1 higher than the degree of the denominator, then it has an slant-asymptote, so this one has a slant-asymptote.

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Pls. see my attachment.

In it I divided the big triangle into two small right triangles.
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