Math Problem Statement

5/2x + 3/x

Solution

The expression you provided is:

52x+3x\frac{5}{2x} + \frac{3}{x}

To simplify or combine this expression, we can find a common denominator.

Step 1: Find the Least Common Denominator (LCD)

The denominators in this expression are 2x2x and xx. The least common denominator (LCD) of these two is 2x2x.

Step 2: Rewrite Each Fraction with the LCD

Now, rewrite each fraction with the common denominator:

52x+3x=52x+32x2=52x+62x\frac{5}{2x} + \frac{3}{x} = \frac{5}{2x} + \frac{3 \cdot 2}{x \cdot 2} = \frac{5}{2x} + \frac{6}{2x}

Step 3: Combine the Fractions

Since both fractions now have the same denominator, you can combine them:

5+62x=112x\frac{5 + 6}{2x} = \frac{11}{2x}

Final Answer:

The simplified form of the expression is:

112x\frac{11}{2x}

Would you like further details or have any questions about this?

Here are 5 related questions you might find interesting:

  1. How would you simplify 73x+2x\frac{7}{3x} + \frac{2}{x}?
  2. What is the least common denominator of 1x\frac{1}{x} and 23x\frac{2}{3x}?
  3. How do you solve the equation 112x=4\frac{11}{2x} = 4 for xx?
  4. What happens if x=0x = 0 in the original expression?
  5. Can you add 5x\frac{5}{x} and 72\frac{7}{2} without finding a common denominator?

Tip: When adding or subtracting fractions, always look for the least common denominator to simplify the process.

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Math Problem Analysis

Mathematical Concepts

Algebra
Fractional Expressions

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9