Question:
Simplify the expression \( \frac{5x}{2x} + \frac{3}{2x} \).
Simplify the expression \( \frac{5x}{2x} + \frac{3}{2x} \).
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When adding fractions with the same denominator, add the numerators directly and keep the denominator unchanged.
Updated On: Oct 4, 2025
- \( \frac{8x}{2x} \)
- \( \frac{13}{2x} \)
- \( \frac{15x}{2x} \)
- \( \frac{13x}{2x} \)
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The Correct Option is B
Solution and Explanation
To add the fractions \(\frac{5x}{2x}\) and \(\frac{3}{2x}\), first note that they already have the same denominator \(2x\). When adding fractions with the same denominator, we keep the denominator and add the numerators:
\[
\frac{5x}{2x} + \frac{3}{2x} = \frac{5x + 3}{2x}.
\]
Next, combine the terms in the numerator:
\[
\frac{5x + 3}{2x}.
\]
Since the problem states that this sum equals \(\frac{13}{2x}\), it shows that the numerator \(5x + 3\) must be equal to 13:
\[
5x + 3 = 13.
\]
You can then solve for \(x\) by subtracting 3 from both sides:
\[
5x = 10,
\]
and dividing both sides by 5:
\[
x = 2.
\]
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