To determine which expressions are equal to [tex]\(0\)[/tex] when [tex]\(x = -1\)[/tex], let us analyze each expression one by one.
1. [tex]\(\frac{4(x+1)}{4x+5}\)[/tex]
Substitute [tex]\(x = -1\)[/tex]:
[tex]\[
\frac{4((-1)+1)}{4(-1)+5} = \frac{4(0)}{-4+5} = \frac{0}{1} = 0
\][/tex]
The first expression is equal to [tex]\(0\)[/tex].
2. [tex]\(\frac{4(x-1)}{5-4x}\)[/tex]
Substitute [tex]\(x = -1\)[/tex]:
[tex]\[
\frac{4((-1)-1)}{5-4(-1)} = \frac{4(-2)}{5+4} = \frac{-8}{9} \neq 0
\][/tex]
The second expression is not equal to [tex]\(0\)[/tex].
3. [tex]\(\frac{4(x-(-1))}{4x+5}\)[/tex]
This simplifies to [tex]\(\frac{4(x+1)}{4x+5}\)[/tex].
Substitute [tex]\(x = -1\)[/tex]:
[tex]\[
\frac{4((-1)+1)}{4(-1)+5} = \frac{4(0)}{-4+5} = \frac{0}{1} = 0
\][/tex]
The third expression is equal to [tex]\(0\)[/tex].
4. [tex]\(\frac{4(x+(-1))}{4x+5}\)[/tex]
This simplifies to [tex]\(\frac{4(x-1)}{4x+5}\)[/tex].
Substitute [tex]\(x = -1\)[/tex]:
[tex]\[
\frac{4((-1)-1)}{4(-1)+5} = \frac{4(-2)}{-4+5} = \frac{-8}{1} \neq 0
\][/tex]
The fourth expression is not equal to [tex]\(0\)[/tex].
5. [tex]\(\frac{4(x+1)}{5-4x}\)[/tex]
Substitute [tex]\(x = -1\)[/tex]:
[tex]\[
\frac{4((-1)+1)}{5-4(-1)} = \frac{4(0)}{5+4} = \frac{0}{9} = 0
\][/tex]
The fifth expression is equal to [tex]\(0\)[/tex].
Thus, the expressions that are equal to [tex]\(0\)[/tex] when [tex]\(x = -1\)[/tex] are:
- [tex]\(\frac{4(x+1)}{4x+5}\)[/tex]
- [tex]\(\frac{4(x-(-1))}{4x+5}\)[/tex]
- [tex]\(\frac{4(x+1)}{5-4x}\)[/tex]
