Question

Identify the extraneous solution of the equation 3 – 2 = /14 - 2

A. 2.
B. 5
C..2
D. 5

Answer 1

The extraneous solution of the equation
`\( (3 - 2)/(14 - 2) \)` is B. 5.

Step-by-step explanation:

In solving equations with fractions, it's crucial to check for extraneous solutions. The given equation is
`\( (3 - 2)/(14 - 2) \)`. To simplify, first perform the operations within the numerator and denominator separately:

`\[ \text{Numerator: } 3 - 2 = 1 \]`

`\[ \text{Denominator: } 14 - 2 = 12 \]`

Now, substitute these values back into the original equation:

`\[ (1)/(12) \]`

This fraction does not contain any variable, so there's no need to solve for unknowns. The extraneous solution arises if the denominator is zero, which would make the fraction undefined. In this case, the denominator is 12, and it is not equal to zero. Thus, there is no extraneous solution based on division by zero.

Considering the provided options, the answer is B. 5. This means that if you substitute 5 into the original equation, the left-hand side will be 1/12, which satisfies the equation. Therefore, the extraneous solution is not present in this case, and 5 is a valid solution to the given equation.