Question

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

Answer 1

To subtract the given rational expressions and express it in the required form, we start with

\[
\frac{x+1}{x+3} - \frac{5}{2x+6}.
\]

1. **Recognize the common denominator**: The expression \( 2x+6 \) can be factored to \( 2(x+3) \).

2. **Rewrite both fractions with a common denominator**: The common denominator between \( x+3 \) and \( 2(x+3) \) is \( 2(x+3) \).

3. **Adjust the first fraction**:
\[
\frac{x+1}{x+3} = \frac{x+1}{x+3} \cdot \frac{2}{2} = \frac{2(x+1)}{2(x+3)} = \frac{2x + 2}{2(x+3)}.
\]

4. **Rewrite the second fraction** with the common denominator:
\[
\frac{5}{2x+6} = \frac{5}{2(x+3)}.
\]

5. **Now subtract the fractions**:
\[
\frac{2x + 2}{2(x+3)} - \frac{5}{2(x+3)} = \frac{(2x + 2) - 5}{2(x+3)} = \frac{2x + 2 - 5}{2(x+3)} = \frac{2x - 3}{2(x+3)}.
\]

Thus, the answer is:

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

So, the missing part in your expression \( \frac{?}{2x+6} \) is \( 2x - 3 \). Therefore:

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