QuestionGiven $f(x)=x^{2}-10 x+25$ and $g(x)=x^{2}-9 x+20$, find $\left(\frac{f}{g}\right)(x)$ and simplify the resulting function.

Studdy Solution
Write the expression $\frac{f(x)}{g(x)}$ using the factored forms:
$$\frac{f(x)}{g(x)} = \frac{(x - 5)^2}{(x - 4)(x - 5)}$$
Cancel the common factor $(x - 5)$ from the numerator and the denominator:
$$\frac{(x - 5)^2}{(x - 4)(x - 5)} = \frac{x - 5}{x - 4}$$
The simplified function is:
$$\frac{f}{g}(x) = \frac{x - 5}{x - 4}$$