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What is the first step in solving the equation below? \( \frac{5}{x-7}=\frac{x}{x+5} \) Square both sides. Subtract 5 from both sides. Add 7 to both sides. Cross multiply 5 times \( x+5 \) and \( x \) times \( x-7 \).

Ask by Peters Weber. in the United States
Mar 12,2025

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The first step is to cross multiply: \( 5(x + 5) = x(x - 7) \).

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The first step in solving the equation \( \frac{5}{x-7}=\frac{x}{x+5} \) is to cross multiply. This means you'll take 5 and multiply it by \( x+5 \) and set it equal to \( x \) multiplied by \( x-7 \). Cross multiplying allows you to eliminate the fractions, simplifying your next steps in solving for \( x \). Remember, cross multiplication works well here because both sides of the equation are fractions. It clears up the equation neatly, allowing you to work with polynomial expressions instead of dealing with the complications of fractions. Just like making a delicious cake, clearing those fractions gives you a smoother batter to work with in your solution process!

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