Final answer:
To simplify an expression from which a common factor of x-9 has been divided out, apply algebraic rules such as eliminating like terms and applying exponent division and multiplication rules.
Step-by-step explanation:
A student has a mathematical expression from which a common factor of x-9 is divided out to obtain a simplified expression. To simplify the expression, we need to identify, isolate, and then divide out the common factor where possible.
The process involves rules of algebraic simplification like eliminating terms where possible and division of exponentials, where you divide the coefficients and subtract the exponents if the bases are the same. For instance, in exponential terms, if you have am / an, you would simplify this to am-n. Similarly, multiplying like bases with exponents, such as am × an, becomes am+n.
Checking the answer to verify if it’s reasonable is also an important step in the simplification process. In the case of xpxq, where you have the same base (x), you would simplify by adding the exponents to get xp+q.