Adding whole number to an algebraic fraction

[morgonia]

I was given some maths homework on Friday but I forgot to write down the technique :x . Can anyone give me the technique for adding a whole number to an algebraic fraction? One of the questions I have is:

.......2x + 1
7+ .........6

 

[morgonia]

I think I'm doing to top line right: change it to

7...........2x + 1
1................6

Now I'm just worried about the bottom line.

 

[Unco]

It's no different to adding adding non-algebraic fractions.

Obtain the lowest common denominator and add the new numerators over that denominator.

\(\displaystyle \L \begin{align*}
\mbox{ \frac{7}{1} + \frac{2x + 1}{6} } &= \mbox{ \frac{7(6)}{6} + \frac{2x + 1}{6} } \\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
&=\mbox{ \frac{42}{6} + \frac{2x + 1}{6} } \\
\\
\\
\\
\\
\\
\\
\\
\\
\\
\\
&=\mbox{ \frac{42 + 2x + 1}{6}}
\end{align*}\)


\(\displaystyle \mbox{ }\) etc.