Questions: Add. [ fracx10+frac3 x8 ] Select the correct choice below and fill in any answer boxes within your choice. (Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) A. (fracx10+frac3 x8=) (square) (x neq) (square) B. (fracx10+frac3 x8=) (square) . no numbers must be excluded.

$Add. [ fracx10+frac3 x8 ] Select the correct choice below and fill in any answer boxes within your choice. (Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) A. (fracx10+frac3 x8=) (square) (x neq) (square) B. (fracx10+frac3 x8=) (square) . no numbers must be excluded.$

Transcript text: Add. \[ \frac{x}{10}+\frac{3 x}{8} \] Select the correct choice below and fill in any answer boxes within your choice. (Simplify your answer. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) A. $\frac{x}{10}+\frac{3 x}{8}=$ $\square$ $x \neq$ $\square$ B. $\frac{x}{10}+\frac{3 x}{8}=$ $\square$ . no numbers must be excluded.

Solution

Solution Steps

To add the fractions $\frac{x}{10}$ and $\frac{3x}{8}$, we need to find a common denominator. The least common multiple of 10 and 8 is 40. We will convert each fraction to have this common denominator and then add them together.

Step 1: Find a Common Denominator

To add the fractions $\frac{x}{10}$ and $\frac{3x}{8}$, we first need to find a common denominator. The denominators are 10 and 8. The least common multiple (LCM) of 10 and 8 is 40.

Step 2: Convert Each Fraction to the Common Denominator

Convert $\frac{x}{10}$ to a fraction with a denominator of 40:

\[ \frac{x}{10} = \frac{x \times 4}{10 \times 4} = \frac{4x}{40} \]

Convert $\frac{3x}{8}$ to a fraction with a denominator of 40:

\[ \frac{3x}{8} = \frac{3x \times 5}{8 \times 5} = \frac{15x}{40} \]

Step 3: Add the Fractions

Now that both fractions have the same denominator, we can add them:

\[ \frac{4x}{40} + \frac{15x}{40} = \frac{4x + 15x}{40} = \frac{19x}{40} \]

Step 4: Simplify the Expression

The fraction $\frac{19x}{40}$ is already in its simplest form since 19 and 40 have no common factors other than 1.

Final Answer

The expression $\frac{x}{10} + \frac{3x}{8}$ simplifies to $\frac{19x}{40}$. Since there are no restrictions on $x$ that would make the denominator zero, the correct choice is:

\[ \boxed{\text{B. } \frac{x}{10} + \frac{3x}{8} = \frac{19x}{40} \text{, no numbers must be excluded.}} \]

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