Question

Divide:

{eq}frac{x^2+6x-44}{x+9}

{/eq}

EXPERT ANSWER

We can simply determine the quotient by using the long division method.

{eq}begin{align}

i.,,,,,,& x + 9 overline{)x^2 +6 x – 44}\[0.2cm]

&,,,,,,,,,,,,,,,,,,,,x\

ii.,,,,,,& x + 9 overline{)x^2 +6 x – 44}\[0.2cm]

&,,,,,,,-underline{(x^2+9x)}\[0.2cm]

&,,,,,,,,,,,,,,,,,,,,x\

iii.,,,,,& x + 9 overline{)x^2 +6 x – 44}\[0.2cm]

&,,,,,,,-underline{(x^2+9x)}\

&,,,,,,,,,,,,,,,,,,,,,,-3x-44\[0.2cm]

&,,,,,,,,,,,,,,,,,,x-3\

iii.,,,,& x + 9 overline{)x^2 +6 x – 44}\[0.2cm]

&,,,,,,,-underline{(x^2+9x)}\

&,,,,,,,,,,,,,,,,,,,,,,-3x-44\

&,,,,,,,,,,,,,,,-underline{(-3x-27)}\

&,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,-17\

end{align}

{/eq}

Therefore,

{eq}color{blue}{dfrac{x^2+6x-44}{x+9} = x-3-dfrac{17}{x+9}}\[0.2cm]

{/eq}

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