Respuesta :

gmany

[tex]f(x)=2x^2-x-6,\ g(x)=x^2-4\\\\f(x)\div g(x)=\dfrac{f(x)}{g(x)}=\dfrac{2x^2-x-6}{x^2-4}=\dfrac{2x^2-4x+3x-6}{x^2-2^2}\\\\=\dfrac{2x(x-2)+3(x-2)}{(x-2)(x+2)}=\dfrac{(x-2)(2x+3)}{(x-2)(x+2)}=\dfrac{2x+3}{x+2}\ for\ x\neq0\\\\Answer:\ f(x)\div g(x)=\dfrac{2x+3}{x+2}[/tex]

[tex]Used:\ a^2-b^2=(a-b)(a+b)[/tex]

xero099

The expression [tex]h(x) = \frac{f(x)}{g(x)}[/tex] is [tex]h(x) = \frac{x + 1.5}{x+2}[/tex].

In this question we apply the concept of Division of Functions, then we Factor and Simplify the resulting expression:

[tex]h(x) = \frac{f(x)}{g(x)}[/tex] (1)

If we know that [tex]f(x) = 2\cdot x^{2} - x - 6[/tex] and [tex]g(x) = x^{2}-4[/tex], then the resulting function is:

[tex]h(x) = \frac{2\cdot x^{2}-x -6}{x^{2}-4}[/tex]

[tex]h(x) = \frac{(x-2)\cdot (x+1.5)}{(x-2)\cdot (x+2)}[/tex]

[tex]h(x) = \frac{x + 1.5}{x+2}[/tex]

The expression [tex]h(x) = \frac{f(x)}{g(x)}[/tex] is [tex]h(x) = \frac{x + 1.5}{x+2}[/tex].

Please see this question related to Function Operations: https://brainly.com/question/22804823

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