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Add the rational expressions:

[tex]\[
\frac{3x + 6}{24} + \frac{2x - 1}{8}
\][/tex]

A. \(\frac{3x + 1}{8}\)

B. \(\frac{3x + 1}{24}\)

C. \(\frac{11x + 2}{24}\)

D. [tex]\(\frac{9x + 3}{8}\)[/tex]

Sagot :

GinnyAnswer
To solve the problem of adding the rational expressions \(\frac{3x + 6}{24}\) and \(\frac{2x - 1}{8}\), follow these steps:

1. Identify the least common denominator (LCD):
- The denominators of the given fractions are 24 and 8.
- The least common denominator of 24 and 8 is 24.

2. Rewrite each fraction with the common denominator:
- The fraction \(\frac{3x + 6}{24}\) already has 24 as the denominator.
- To rewrite \(\frac{2x - 1}{8}\) with 24 as the denominator, express it in terms of 24:
[tex]\[ \frac{2x - 1}{8} = \frac{2x - 1}{8} \times \frac{3}{3} = \frac{3(2x - 1)}{24} = \frac{6x - 3}{24} \][/tex]

3. Add the fractions:
- Now, add the two fractions:
[tex]\[ \frac{3x + 6}{24} + \frac{6x - 3}{24} = \frac{(3x + 6) + (6x - 3)}{24} = \frac{3x + 6 + 6x - 3}{24} = \frac{9x + 3}{24} \][/tex]

4. Simplify the result:
- Simplify the numerator if possible:
[tex]\[ \frac{9x + 3}{24} = \frac{3(3x + 1)}{24} \][/tex]
- Recognize that the greatest common divisor (GCD) of 3 and 24 is 3, so we divide both the numerator and the denominator by 3:
[tex]\[ \frac{3(3x + 1)}{24} = \frac{3x + 1}{8} \][/tex]

Therefore, the simplified form of the sum [tex]\(\frac{3x + 6}{24} + \frac{2x - 1}{8}\)[/tex] is [tex]\(\boxed{\frac{3x + 1}{8}}\)[/tex].
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