Question

1. \\(\frac{x + 2}{2x + 2} + \frac{6}{2}\\)

Explanation:

Step1: Simplify the first fraction

Factor the denominator of the first fraction: \(2x + 2 = 2(x + 1)\), and the numerator is \(x + 2\), so the first fraction \(\frac{x + 2}{2x + 2}=\frac{x + 2}{2(x + 1)}\).

Step2: Simplify the second fraction

The second fraction \(\frac{6}{2}\) simplifies to \(3\).

Step3: Combine the two terms

Now we have \(\frac{x + 2}{2(x + 1)}+3\). To combine them, we can write \(3\) as \(\frac{3\times2(x + 1)}{2(x + 1)}=\frac{6(x + 1)}{2(x + 1)}\). Then add the two fractions: \(\frac{x + 2+6(x + 1)}{2(x + 1)}\).

Step4: Expand and simplify the numerator

Expand the numerator: \(x + 2+6x + 6 = 7x + 8\). So the simplified form is \(\frac{7x + 8}{2(x + 1)}\) (or we can also write it as \(\frac{7x + 8}{2x + 2}\) by distributing the \(2\) in the denominator).

Answer:

\(\frac{7x + 8}{2x + 2}\) (or \(\frac{7x + 8}{2(x + 1)}\))