Question

m(x) = x² + 4x
n(x) = x
(mn)(x) =
x² + 4x(x)
(x² + 4x)(x) ✔
complete
which is equal to:
x³ + 4x² ✔
5x²
4x⁴
complete
evaluate (mn)(x) for x = -3.
(mn)(-3) = 9 ✔
complete
(m/n)(x), x ≠ 0 ✔
complete
evaluate (m/n)(x) for x = -3.
(m/n)(-3) =

Explanation:

Step1: Find the expression for \(\frac{m}{n}(x)\)

Given \(m(x)=x^{2}+4x\) and \(n(x)=x\) (\(x
eq0\)), then \(\frac{m}{n}(x)=\frac{x^{2}+4x}{x}\). We can simplify this by factoring out \(x\) from the numerator: \(\frac{x(x + 4)}{x}\). Since \(x
eq0\), we can cancel out the \(x\) terms, so \(\frac{m}{n}(x)=x + 4\).

Step2: Evaluate \(\frac{m}{n}(-3)\)

Substitute \(x=-3\) into the simplified expression \(x + 4\). So we have \(-3+4\).

Step3: Calculate the result

\(-3 + 4=1\).

Answer:

\(1\)