*simplifying rational expressions
a. 6x+12/4-x
b. 3x^2/12-2x
To simplify rational expressions, we need to simplify both the numerator and the denominator separately and then simplify the resulting expression.
Let's start with the expression (a) 6x + 12 / 4 - x:
1. Simplify the numerator: Since there are no common factors between 6x and 12, we cannot simplify it further.
2. Simplify the denominator: The denominator is 4 - x. To simplify this, we can change the order of subtraction to addition and distribute a negative sign: -x + 4.
3. Combine like terms: Since both the numerator and the denominator have no like terms, we can leave them as they are.
So the simplified expression becomes: (6x + 12) / (-x + 4).
Now, let's simplify expression (b) 3x^2 / 12 - 2x:
1. Simplify the numerator: The numerator is 3x^2. Since there are no factors common to 3 and x^2, we cannot simplify it further.
2. Simplify the denominator: The denominator is 12 - 2x. Again, we can rearrange the subtraction to addition and distribute a negative sign: -2x + 12.
3. Combine like terms: Since the numerator and denominator have no common terms, we leave them unchanged.
The simplified expression is: 3x^2 / (-2x + 12).
Remember that these expressions are already simplified as much as possible. If there are any additional simplification possibilities, it would depend on specific instructions given or any restrictions on the variables.