Question

Subtract the following rational expressions.
x+1/x+3 - 5/2x+6= /2x+6

Answer 1

To subtract the rational expressions \(\frac{x + 1}{x + 3} - \frac{5}{2x + 6}\), we first need to find a common denominator.

The second fraction can be simplified since \(2x + 6\) can be factored:

\[
2x + 6 = 2(x + 3)
\]

So the expression becomes:

\[
\frac{x + 1}{x + 3} - \frac{5}{2(x + 3)}
\]

Now, we can see that the common denominator is \(2(x + 3)\). We will rewrite both fractions with this common denominator:

1. The first fraction:

\[
\frac{x + 1}{x + 3} = \frac{(x + 1) \cdot 2}{2(x + 3)} = \frac{2(x + 1)}{2(x + 3)} = \frac{2x + 2}{2(x + 3)}
\]

2. The second fraction is already in the desired form:

\[
\frac{-5}{2(x + 3)}
\]

Now we can combine the two fractions:

\[
\frac{2x + 2 - 5}{2(x + 3)} = \frac{2x + 2 - 5}{2(x + 3)} = \frac{2x - 3}{2(x + 3)}
\]

Thus, the result of the subtraction is:

\[
\frac{2x - 3}{2(x + 3)}
\]