Answered

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Express the sum in the simplest form:

[tex]\[
\frac{x}{x+5}+\frac{5}{x+5}
\][/tex]

A. [tex]\(\frac{5x}{x+5}\)[/tex]

B. [tex]\(\frac{x}{x+5}\)[/tex]

C. [tex]\(\frac{5}{x+5}\)[/tex]

D. 1

Sagot :

GinnyAnswer
To express the sum [tex]\(\frac{x}{x+5} + \frac{5}{x+5}\)[/tex] in its simplest form, we need to combine the two fractions since they have the same denominator.

Given the expression:
[tex]\[ \frac{x}{x+5} + \frac{5}{x+5} \][/tex]

Step 1: Combine the numerators over the common denominator.
The fractions share the same denominator [tex]\((x+5)\)[/tex], so we can add the numerators directly:
[tex]\[ \frac{x + 5}{x+5} \][/tex]

Step 2: Simplify the fraction.
Notice that both the numerator and denominator contain the term [tex]\((x+5)\)[/tex]:
[tex]\[ \frac{x+5}{x+5} = 1 \][/tex]

Thus, the simplified form of the expression [tex]\(\frac{x}{x+5} + \frac{5}{x+5}\)[/tex] is:
[tex]\[ \boxed{1} \][/tex]
So the correct answer is [tex]\(D\)[/tex].
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