Question

Just apart of a homework practice. Is the answer option A or D?

Answer 1

`4x-3,x\\e-5`

Step-by-step explanation

`\begin{gathered} f(x)=4x^2+17x-15 \\ g(x)=x+5 \end{gathered}`

find

`(f(x))/(g(x))=(4x^2+17x-15)/(x+1)`

Step 1

factorize the numerator.

so

`\begin{gathered} 4x^2+17x-15 \\ \text{rewrite 17x as}-3x+20x \\ 4x^2-3x+20x-15 \\ group \\ (4x^2-3x)+(20x-15) \\ x(4x-3)+5(4x-3) \\ \text{hence} \\ (x+5)(4x-3) \\ 4x^2+17x-15=(x+5)(4x-3) \end{gathered}`

Step 2

replace

`\begin{gathered} (f(x))/(g(x))=(4x^2+17x-15)/(x+5) \\ (f(x))/(g(x))=((x+5)(4x-3))/(x+5) \\ (x+5)\text{ is eliminated,therefore} \\ (f(x))/(g(x))=(4x-3) \end{gathered}`

so, the answer is

`4x-3`

but, we have the restriction, the denominator cannot be zero, so

`\begin{gathered} (f(x))/(g(x))=((x+5)(4x-3))/(x+5) \\ x+5\\e0 \\ x\\e-5 \end{gathered}`

therefore, the solution is

`4x-3,x\\e-5`

D)

I hope this helps you