Question

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​

Answer 1

`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) \\ (f(x))/(g(x)) = ((2x + 3)(x - 2))/((x + 2)(x - 2)) = (2x + 3)/(x + 2)`

Answer 2

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

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

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)}`

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

`\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 \: \: }}}`