Question

14 fill in the blank 1 point
given the function $f(x)=x^2 + 5x + 10$ and $g(x)=x + 3$, then:
$\frac{f(x)}{g(x)}=x + 2+\frac{c}{x+3}$
for what value of c? type your answer...

Explanation:

Step1: Combine right-hand side terms

$$\frac{f(x)}{g(x)} = \frac{(x+2)(x+3) + c}{x+3}$$

Step2: Expand numerator on right

$$\frac{f(x)}{g(x)} = \frac{x^2 + 5x + 6 + c}{x+3}$$

Step3: Equate numerators to f(x)

$$x^2 + 5x + 10 = x^2 + 5x + 6 + c$$

Step4: Solve for c

$$c = 10 - 6 = 1$$

Answer:

1