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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​

Sagot :

Answer:

[tex]f(x) = {2x}^{2} - 4x - 6 \\ {2x}^{2} - 4x + 3x - 6 \\ = 2x(x - 2) + 3(x - 2) \\ g(x) = {x}^{2} - 4 \\ (x + 2)(x - 2) \\ \frac{f(x)}{g(x)} = \frac{(2x + 3)(x - 2)}{(x + 2)(x - 2)} = \frac{2x + 3}{x + 2} [/tex]

Relaxgrow

[tex]\underline{\underline{\boxed{ \pink\star \: C.) \: \sf{\frac{2x +3}{x + 2}}}}}[/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Here,

[tex]\sf{f(x) = 2x^2 - x - 6}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\longrightarrow\sf{2x^2 - 4x + 3x - 6}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\longrightarrow\sf{2x(x-2)+3(x-2)}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\longrightarrow\sf{(2x+3)(x-2)}[/tex]

---------------------------------------------------

[tex]\sf{g(x) = x^2 - 4}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\longrightarrow\sf{x^2 - 2^2}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\longrightarrow\sf{(x+2)(x-2)}[/tex]

Therefore,

[tex]\huge\sf{ \frac{f(x)}{g(x)} = \frac{(2x+3)(x-2)}{(x+2)(x-2)}}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\longrightarrow \huge\sf{ \frac{2x + 3}{x + 2}}[/tex]

[tex]\boxed{\underline{\color{hotpink}{ \red \star \: ᖇEᒪᗩ᙭GᖇOᗯ \: \: }}}[/tex]

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