After multiplying by $x+3$, you will get $(x+3)\bigl(x+4+\frac{9}{x+3}\bigr)$. Distribute $(x+3)$ across each term in the parentheses and simplify, paying attention to how $(x+3)$ interacts with $\frac{9}{x+3}$.

Once you have written the right-hand side as a standard quadratic (like $x^2 + 7x + 21$ but with your values), set it equal to $x^2 + bx + c$ and match the coefficients of $x$ and the constant term to identify $b$ and $c$.

In a blank expression line, type (x+4)*(x+3)+9. Desmos will automatically simplify this product and sum, showing an expanded quadratic expression next to what you typed.

Compare the simplified expression Desmos shows (it will look like x^2 + (number)x + (number)) to $x^2 + bx + c$ and read off the values of $b$ (the coefficient of $x$) and $c$ (the constant term). Then add these two numbers to get $b+c$.

Because the two expressions are equivalent for all $x \neq -3$, their values must match whenever $x$ is allowed. Multiply both sides by $x+3$ to remove the denominator:

becomes

Now simplify the right-hand side.

Distribute $(x+3)$ across the sum inside the parentheses:

The second term simplifies because $x+3$ cancels:

Now expand $(x+3)(x+4)$:

So the entire right-hand side is

You now have

Since these polynomials are equal for all $x$, their corresponding coefficients must be equal:

• Coefficient of $x$: $b = 7$
• Constant term: $c = 21$

Therefore,

So the correct answer is 28.