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Difficulty: EasyRational and Radical Expressions and Equations

Determine the value of xx for which the given rational expression is undefined.

Answer:The rational expression x+72x−10\frac{x + 7}{2x - 10} is undefined when x=x = 【5】.

Answer

5
The rational expression is undefined when the denominator, 2x−102x - 10, equals 00. Solving 2x−10=02x - 10 = 0 gives 2x=102x = 10, which simplifies to x=5x = 5.

Step-by-Step Solution

1
Identify the denominator of the rational expression and set it equal to zero.
2x−10=02x - 10 = 0
A rational expression is undefined when its denominator is equal to zero, as division by zero is not defined in the real number system.
2
Solve the linear equation for xx by adding 10 to both sides and then dividing by 2.
2x=10⇒x=52x = 10 \Rightarrow x = 5
Isolating xx yields the value that makes the denominator zero.

Key Concept

Rational expressions are undefined when the denominator is equal to zero.
Estimated Time:45s
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Topics

Rational and Radical Expressions and Equations

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