Let's solve the given expression step-by-step.
The problem is:
[tex]\[
\frac{6x(x+y)}{x+y} - \frac{2(x+y)}{x+y}
\][/tex]
### Step 1: Simplify the Expression
First, observe that the terms [tex]\((x+y)\)[/tex] in the numerator and denominator can cancel out in both fractions:
[tex]\[
\frac{6x(x+y)}{x+y} - \frac{2(x+y)}{x+y} \implies 6x - 2
\][/tex]
By cancelling out the common terms, we directly simplify the expression to:
[tex]\[
6x - 2
\][/tex]
### Step 2: Factorize the Simplified Expression
Next, we will factorize the simplified expression [tex]\(6x - 2\)[/tex]. To do this, we look for common factors in the terms. Both terms have a common factor of 2:
[tex]\[
6x - 2 = 2(3x - 1)
\][/tex]
Therefore, the factored form of [tex]\(6x - 2\)[/tex] is:
[tex]\[
2(3x - 1)
\][/tex]
### Final Summary
- Original Expression: [tex]\(\frac{6x(x+y)}{x+y} - \frac{2(x+y)}{x+y}\)[/tex]
- Simplified Expression: [tex]\(6x - 2\)[/tex]
- Factored Expression: [tex]\(2(3x - 1)\)[/tex]
So the succession of transformations is:
1. Given expression: [tex]\(\frac{6x(x+y)}{x+y} - \frac{2(x+y)}{x+y}\)[/tex]
2. Simplified to: [tex]\(6x - 2\)[/tex]
3. Factored form: [tex]\(2(3x-1)\)[/tex]
