Certainly! Let's simplify the given expression step-by-step.
Given the expression:
[tex]\[ 5^{1-x} + 5^{x-1} - 5 \cdot \frac{1}{5} \][/tex]
Step 1: Simplify the constant term.
[tex]\[ 5 \cdot \frac{1}{5} = 1 \][/tex]
So the expression becomes:
[tex]\[ 5^{1-x} + 5^{x-1} - 1 \][/tex]
Step 2: Observe the behavior of the exponents.
Notice that:
[tex]\[ 5^{x-1} \][/tex]
can also be written using properties of exponents as:
[tex]\[ \frac{1}{5^{1-x}} \][/tex]
However, for simplification, we do not need to change this. We keep it as it is:
[tex]\[ 5^{1-x} \text{ and } 5^{x-1} \][/tex]
Step 3: Observing the final form and combining terms:
There are no like terms to combine, so we keep the terms as they are.
Thus, the expression simplifies to:
[tex]\[ 5^{1 - x} + 5^{x - 1} - 1 \][/tex]
So, the simplified expression is:
[tex]\[ \boxed{5^{1 - x} + 5^{x - 1} - 1} \][/tex]
