Question
Fill in the blank to make equivalent rational expressions. \[ \frac{8}{x+9}=\frac{\square}{(x+2)(x+9)} \]
Ask by Riley Cummings. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression in the box is \( 8(x + 2) \).
Solution
To make the expressions equivalent, multiply the left side's numerator and denominator by (x + 2):
8/(x + 9) = [8(x + 2)]/[(x + 2)(x + 9)].
Thus, the expression in the box is 8(x + 2).
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Simplify this solution Mind Expander
To make the two rational expressions equivalent, we need to find a value for the blank that when the first expression is cross-multiplied, it results in the product. The right side has \((x+2)(x+9)\) in the denominator, so we multiply the numerator 8 by \((x+2)\) to maintain equivalence. Thus, we fill in the blank with: \[ 8(x+2) \] So the complete expression would be: \[ \frac{8}{x+9} = \frac{8(x+2)}{(x+2)(x+9)} \]
