Question

Subtract the rational expressions and give the answer in simplest form.5x2+5x+6−2(x+2)

Answer 1

To subtract the rational expressions \( 5x^2 + 5x + 6 - 2(x + 2) \), we first simplify the expression by distributing and combining like terms.

1. Distribute \( -2 \) to \( (x + 2) \):
\[
-2(x + 2) = -2x - 4
\]

2. Now substitute this back into the expression:
\[
5x^2 + 5x + 6 - 2x - 4
\]

3. Next, combine like terms:
- Combine \( 5x \) and \( -2x \):
\[
5x - 2x = 3x
\]
- Combine \( 6 \) and \( -4 \):
\[
6 - 4 = 2
\]

Putting it all together, we have:
\[
5x^2 + 3x + 2
\]

Thus, the final result in simplest form is:
\[
\boxed{5x^2 + 3x + 2}
\]