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Chapter 7: Problem 62

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{5 x-4}{4-5 x}$$

Short Answer

Expert verified
The simplified form of the rational expression \( \frac{5x-4}{4-5x} \) is -1. Note: This is valid only when \( x \neq \frac{4}{5} \) to avoid division by zero.

Step by step solution

01

Observe Reflexive Rule

An application of the reflexive rule of operations on the given expression \( \frac{5x-4}{4-5x} \). The reflexive rule states that the order of subtraction does not affect the absolute value of the difference between two numbers. So, \( 5x - 4 = -(4 - 5x) \) and also \( 5x - 4 = -(-4 + 5x) \).
02

Apply Reflexive Rule

So, the original expression can be written as, \( \frac{5x - 4}{4 - 5x} = \frac { -(-4 + 5x)}{4 - 5x} = -1 \), because \( \frac{a}{a} = 1 \), where \( a \) can be any expression, but \( a \neq 0 \).

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