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Chapter 0: Problem 98

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I evaluated \(\frac{3 x-3}{4 x(x-1)}\) for \(x=1\) and obtained 0.

Short Answer

Expert verified
The given statement 'I evaluated \(\frac{3x - 3}{4x(x - 1)}\) for \(x = 1\) and obtained 0.' does not make sense, as division by zero is undefined in mathematics. Therefore, one cannot evaluate the function at \(x = 1\).

Step by step solution

01

Understand the Function

The function we are to evaluate is \(\frac{3x - 3}{4x(x - 1)}\). This is a rational function, a ratio of two polynomials.
02

Substitution

Next, we will substitute \(x = 1\) into this function, to obtain \(\frac{3*1 - 3}{4*1*(1 - 1)}\).
03

Evaluate the Expression

Simplifying the above expression, we get 0 in the numerator and also 0 in the denominator, which is a division by zero situation.
04

Determine the Result

In mathematics, division by zero is undefined. Hence, the rational function \(\frac{3x - 3}{4x(x - 1)}\) is undefined at \(x = 1\).

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