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Answer :
The function f(x) = x/(x-5) ÷ 4/(x-8) simplifies to f(x) = x/4.
The function f(x) = x/(x-5) ÷ 4/(x-8) involves rational expressions. To simplify this expression, we can follow these steps:
Step 1: Simplify the expression within the division symbol (÷).
- The expression x/(x-5) can be rewritten as x * (x-8)/4.
- The expression 4/(x-8) remains the same.
Step 2: Multiply the two rational expressions.
- (x * (x-8)/4) * (4/(x-8))
Step 3: Cancel out common factors.
- The factor (x-8) appears in both the numerator and denominator, so it cancels out.
Step 4: Simplify the remaining expression.
- We are left with x * 1/4.
- This simplifies to x/4.
Therefore, the function f(x) = x/(x-5) ÷ 4/(x-8) simplifies to f(x) = x/4.
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