Simplify the following rational expressions by factoring and canceling. And define the constraints (what 𝓧 cannot be) (show all work):

Question

38x-48x2-14x+48x-8

Answer 1

To simplify the expression \(38x - 48x^2 - 14x + 48x - 8\), let's first combine like terms.

1. Combine Like Terms: \[ 38x - 14x + 48x - 48x - 8 \] \[ = (38x - 14x + 48x - 48x) - 8 \] \[ = (38 - 14 + 48 - 48)x - 8 \] \[ = 24x - 8 \]

2. Factor the Expression: Now, we can factor out the common factor from the expression \(24x - 8\). \[ = 8(3x - 1) \]

3. Define Constraints: We need to consider any restrictions on \(x\) from the original expression. In this case, it appears there are no denominators or roots that would impose restrictions. Therefore, there are no constraints from this expression.

Thus, the simplified form of the expression is: \[ 8(3x - 1) \]

And since there are no restrictions on the variable \(x\) in this expression, we conclude that: \[ \text{Constraints: } x \in \mathbb{R} \text{ (all real numbers)} \]