Question
Fill in the blank to make equivalent rational expressions. \( \frac{3}{y^{4}}=\frac{\square}{2 y^{6}} \)
Ask by Franklin Howell. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The blank should be filled with \( 6y^{2} \).
Solution
We want to find a number (or expression) in the blank such that
3/y⁴ = (□)/(2y⁶).
Step 1: Start with the equation
3/y⁴ = N/(2y⁶) (where N is the expression in the blank)
Step 2: Multiply both sides of the equation by 2y⁶ to solve for N:
N = (3/y⁴) × (2y⁶).
Step 3: Simplify the expression:
N = 6y^(6-4) = 6y².
Therefore, the rational expression that is equivalent is
3/y⁴ = (6y²)/(2y⁶).
So, the blank should be filled with 6y².
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Simplify this solution Mind Expander
To create equivalent rational expressions, you can cross-multiply. The equation \( \frac{3}{y^{4}}=\frac{\square}{2 y^{6}} \) means you can set up the equation: \( 3 \cdot 2 y^{6} = \square \cdot y^{4} \). This simplifies to \( 6y^{6} = \square \cdot y^{4} \). Now, divide both sides by \( y^{4} \) (assuming \( y \neq 0 \)): \(\square = 6y^{2}.\) So the expression is \( \frac{3}{y^{4}}=\frac{6y^{2}}{2y^{6}} \). Don't forget, when working with rational expressions, ensure that you're upholding any restrictions on variables to avoid division by zero!
