Problem 62
Question
Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{5 x-4}{4-5 x}$$
Step-by-Step Solution
Verified Answer
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.
1Step 1: 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 \( 5x - 4 = -(-4 + 5x) \).
2Step 2: 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 \( a \neq 0 \).
Other exercises in this chapter
Problem 61
Divide as indicated. $$\frac{x^{2}-y^{2}}{8 x^{2}-16 x y+8 y^{2}} \div \frac{4 x-4 y}{x+y}$$
View solution Problem 62
denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{2 y}{x^{2}-y^{2}}+\frac{2 x}{y^{2}-x^{
View solution Problem 62
Determine whether statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(\frac{\frac{1}{4}-\frac{1}{
View solution Problem 62
Add or subtract as indicated. Simplify the result, if possible. $$\frac{2 x-1}{x+6}-\frac{6-5 x}{x^{2}-36}$$
View solution