To correctly divide the expression [tex]\( 12x^2 + 4x \)[/tex] by 2 using the fraction method, you should follow these steps:
1. Separate the Terms: When you have an expression in the form of [tex]\( \frac{a + b}{c} \)[/tex], you can break it down into [tex]\( \frac{a}{c} + \frac{b}{c} \)[/tex]. Here, [tex]\( a \)[/tex] is [tex]\( 12x^2 \)[/tex], [tex]\( b \)[/tex] is [tex]\( 4x \)[/tex], and [tex]\( c \)[/tex] is 2.
So, the expression [tex]\( \frac{12x^2 + 4x}{2} \)[/tex] can be split into [tex]\( \frac{12x^2}{2} + \frac{4x}{2} \)[/tex].
2. Divide Each Term Separately: Next, divide each term in the numerator by the denominator separately.
- For the first term, [tex]\( \frac{12x^2}{2} \)[/tex], divide the coefficient (12) by 2:
[tex]\[
\frac{12x^2}{2} = 6x^2
\][/tex]
- For the second term, [tex]\( \frac{4x}{2} \)[/tex], divide the coefficient (4) by 2:
[tex]\[
\frac{4x}{2} = 2x
\][/tex]
3. Simplify the Expression: After performing the division for each term, write down the resulting expression.
Combining these results, you get:
[tex]\[
6x^2 + 2x
\][/tex]
Given the options provided:
- [tex]\(\frac{12 x^2}{2}+\frac{4 x}{2}\)[/tex]
- [tex]\(\frac{2}{12 x^2}+\frac{2}{4 x}\)[/tex]
The first option [tex]\(\frac{12 x^2}{2}+\frac{4 x}{2}\)[/tex] shows the correct next step for dividing [tex]\( 12x^2 + 4x \)[/tex] by 2 using the fraction method, as it correctly separates the terms in the numerator to be individually divided by the denominator.
So, the correct next step is indeed:
[tex]\[
\frac{12x^2}{2} + \frac{4x}{2}
\][/tex]
