Problem 98 - College Algebra Essentials

Question

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.

Step-by-Step Solution

Answer

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 1: 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.

Step 2: Substitution

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

Step 3: 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.

Step 4: Determine the Result

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