Sure, let's work through the solution step-by-step.
We need to find the quotient of the expression [tex]\(\frac{6x^2 + 9x}{3x}\)[/tex].
1. Rewrite the expression:
Split the given expression into its individual terms divided by [tex]\(3x\)[/tex]:
[tex]\[
\frac{6x^2}{3x} + \frac{9x}{3x}
\][/tex]
2. Simplify each term:
- For the first term [tex]\(\frac{6x^2}{3x}\)[/tex]:
[tex]\[
\frac{6x^2}{3x} = 2x
\][/tex]
(Here, [tex]\(6x^2 \div 3x\)[/tex] simplifies to [tex]\(2x\)[/tex] because [tex]\(6 \div 3 = 2\)[/tex] and [tex]\(x^2 \div x = x\)[/tex])
- For the second term [tex]\(\frac{9x}{3x}\)[/tex]:
[tex]\[
\frac{9x}{3x} = 3
\][/tex]
(Here, [tex]\(9x \div 3x\)[/tex] simplifies to [tex]\(3\)[/tex] because [tex]\(9 \div 3 = 3\)[/tex] and [tex]\(x \div x = 1\)[/tex])
3. Combine the simplified terms:
Putting it all together:
[tex]\[
\frac{6x^2 + 9x}{3x} = 2x + 3
\][/tex]
So, the quotient of the expression [tex]\(\frac{6x^2 + 9x}{3x}\)[/tex] is [tex]\(2x + 3\)[/tex].
