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What is the value of the rational expression [tex]\frac{6-x}{x+5}[/tex] when [tex]x=2[/tex]?

A. [tex]\frac{4}{7}[/tex]
B. [tex]\frac{4}{5}[/tex]
C. [tex]\frac{8}{7}[/tex]
D. [tex]\frac{8}{5}[/tex]


Sagot :

To determine the value of the rational expression [tex]\(\frac{6-x}{x+5}\)[/tex] when [tex]\(x = 2\)[/tex], we will follow these steps:

1. Substitute [tex]\(x = 2\)[/tex] into the expression:

[tex]\[ \frac{6-2}{2+5} \][/tex]

2. Simplify the numerator:

[tex]\[ 6 - 2 = 4 \][/tex]

3. Simplify the denominator:

[tex]\[ 2 + 5 = 7 \][/tex]

4. Write the simplified form of the rational expression:

[tex]\[ \frac{4}{7} \][/tex]

Therefore, when [tex]\(x = 2\)[/tex], the value of the rational expression [tex]\(\frac{6-x}{x+5}\)[/tex] is [tex]\(\frac{4}{7}\)[/tex].

Thus, the correct option is [tex]\(\frac{4}{7}\)[/tex].