Respuesta :

Space

Answer:

Restrictions: x ≠ 0, 3

The value of x is equal to 5.

General Formulas and Concepts:

Pre-Algebra

  • Distributive Property

Algebra I

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality

Terms/Coefficients

  • Expanding/Factoring

Domain

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle \frac{2}{x - 3} = \frac{5}{x}[/tex]

Step 2: Examine

Since we have an x - 3 and x in the denominator, we must make sure the denominator cannot equal 0, or that would get us an undefined answer. Therefore, our restrictions are that x ≠ 0, 3.

Step 3: Solve for x

  1. [Multiplication Property of Equality] Cross-multiply:
    [tex]\displaystyle 2x = 5(x - 3)[/tex]
  2. [Distributive Property] Distribute 5:
    [tex]\displaystyle 2x = 5x - 15[/tex]
  3. [Subtraction Property of Equality] Subtract 5x on both sides:
    [tex]\displaystyle -3x = -15[/tex]
  4. [Division Property of Equality] Divide -3 on both sides:
    [tex]\displaystyle x = 5[/tex]

Since 5 is not equal to 0 or 3, it can be our solution.

∴ we have found the value of x from the given rational function.

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Topic: Algebra I

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