An apprentice electrician is calculating the voltage drop in a circuit using a formula that results in the expression $\frac{4 - \sqrt{48}}{2}$. To confirm the result, the apprentice simplifies the expression step-by-step. Match each part of the expression with its correctly simplified or factored form based on the standard simplification procedure.

A machinist is calculating the depth of a precision cut and arrives at the expression $\frac{4 - \sqrt{48}}{2}$ millimeters. To ensure the final specifications are as simple as possible, what is the correct simplified form of this expression?

An industrial technician is documenting the standard procedure for simplifying a precision measurement formula that results in the expression $\frac{4 - \sqrt{48}}{2}$. Arrange the following steps in the correct order to move from the initial expression to the final simplified result.

Standard Procedure for Simplifying Radical Fractions

A manufacturing technician is calculating an accepted variance for a machine part, which results in the expression $\frac{4 - \sqrt{48}}{2}$. According to standard algebraic procedures, they must first factor out a common factor from the entire numerator before canceling any numbers with the denominator.

A quality assurance analyst is using a standard formula to determine material tolerances, which results in the fraction $\frac{4 - \sqrt{48}}{2}$. After simplifying the radical to ${}4\sqrt{3}$, the numerator becomes ${}4 - 4\sqrt{3}$. To properly simplify the fraction further, the greatest common factor that must be factored out of the entire numerator before canceling with the denominator is ____.

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