Question

Name the restrictions on x then solve showing your steps. 2/(x-3)= 5/x

Answer 1

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

Explanation:

Step 1: Define

Identify given.

`\displaystyle (2)/(x - 3) = (5)/(x)`

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

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