Select the correct answer. If f(x)=2x^2-x-6 and g(x)=x^2-4, find f(x) ÷ g(x) A, 2x + 3/x - 2 B. 2x - 3/x+ 2 C. 2x +3/x+2 D. 2x- 3/x-2

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asked Jan 26, 2023 76.6k views

2 Answers

Alan Mulligan · Answer 1 · 2023-02-01T13:48:17+0000

$\underline{\underline{\boxed{ \pink\star \: C.) \: \sf{(2x +3)/(x + 2)}}}}$

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Here,

$\sf{f(x) = 2x^2 - x - 6}$

$\: \: \: \: \: \: \: \: \: \: \:$

$\longrightarrow\sf{2x^2 - 4x + 3x - 6}$

$\: \: \: \: \: \: \: \: \: \: \:$

$\longrightarrow\sf{2x(x-2)+3(x-2)}$

$\: \: \: \: \: \: \: \: \: \: \:$

$\longrightarrow\sf{(2x+3)(x-2)}$

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$\sf{g(x) = x^2 - 4}$

$\: \: \: \: \: \: \: \: \: \: \:$

$\longrightarrow\sf{x^2 - 2^2}$

$\: \: \: \: \: \: \: \: \: \: \:$

$\longrightarrow\sf{(x+2)(x-2)}$

Therefore,

$\huge\sf{ (f(x))/(g(x)) = ((2x+3)(x-2))/((x+2)(x-2))}$

$\: \: \: \: \: \: \: \: \: \: \:$

$\longrightarrow \huge\sf{ (2x + 3)/(x + 2)}$

$\boxed{\underline{\color{hotpink}{ \red \star \: ᖇEᒪᗩ᙭GᖇOᗯ \: \: }}}$