Question

Simplify the expression: \( \frac{3x - 4}{x} + \frac{2x + 5}{x} \). Options

• A. \( \frac{5x + 1}{x} \)
• B. \( 5 + \frac{1}{x} \)
• C. \( \frac{5}{x} + 1 \)
• D. \( \frac{1}{x} - 5 \)

Hint:

When adding algebraic fractions with the same denominator, combine the numerators first, then simplify.

Answer 1

The Correct Option is B

We are tasked with simplifying the sum of two fractions. The two fractions have the same denominator, so we can combine them directly. Step 1: Combine the fractions.
The two fractions are \( \frac{3x - 4}{x} \) and \( \frac{2x + 5}{x} \), which share the same denominator \( x \). To combine them, we add the numerators and keep the common denominator: \[ \frac{3x - 4}{x} + \frac{2x + 5}{x} = \frac{(3x - 4 + 2x + 5)}{x}. \]
[6pt] Step 2: Simplify the numerator.
Now simplify the numerator by combining like terms: \[ 3x + 2x = 5x
\text{and}
-4 + 5 = 1. \] So, the expression becomes: \[ \frac{5x + 1}{x}. \]
[6pt] Step 3: Simplify the expression further.
We can now split the fraction into two parts: \[ \frac{5x + 1}{x} = \frac{5x}{x} + \frac{1}{x}. \] Simplify each term: \[ \frac{5x}{x} = 5
\text{and}
\frac{1}{x} \text{ stays as is}. \] Thus, the expression becomes: \[ 5 + \frac{1}{x}. \]
[6pt] Conclusion:
The simplified expression is: \[ \boxed{5 + \frac{1}{x}}. \] This is the final simplified form of the given expression.