Simplify the expression.
$\frac{-9 a+9 b}{a-b}$
Select the correct choice below and fill in any answer boxes in your choice.
A. $\frac{-9 a+9 b}{a-b}=$ $\square$ (Simplify your answer.)
B. The expression cannot be simplified.
Answer (1)
Factor out -9 from the numerator, cancel the common factor (a-b) from the numerator and the denominator, and simplify the expression to -9. The simplified expression is − 9 .
Explanation
Simplifying the Expression We are asked to simplify the expression a − b − 9 a + 9 b .
First, we can factor out a − 9 from the numerator: − 9 a + 9 b = − 9 ( a − b )
So the expression becomes: a − b − 9 ( a − b )
Now, we can cancel the common factor ( a − b ) from the numerator and the denominator, assuming a = b :
a − b − 9 ( a − b ) = − 9
Thus, the simplified expression is − 9 .
Examples
Simplifying algebraic expressions is a fundamental skill in mathematics with applications in various fields. For example, in physics, you might need to simplify an expression representing the force acting on an object. Suppose the force is given by F = x − y k ( x − y ) , where k is a constant. Simplifying this expression to F = k makes it easier to calculate the force for different values of k . This skill is also useful in economics, engineering, and computer science, where complex formulas often need to be simplified for efficient computation and analysis.
