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4. Simplify the expression:
[tex]\[ \frac{6x(x+y)}{x+y} - \frac{2(x+y)}{x+y} \][/tex]

(Hint: Factor out [tex]\((x+y)\)[/tex])

[tex]\[ \frac{(x+y)(6x-2)}{(x+y)} \][/tex]

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This provides a clear and easy-to-read question along with a hint to help the student approach the problem.

Sagot :

GinnyAnsweridn
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]
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