×/5+1/4=×/2 can you solve using solving Rational?

Let's solve the equation \( \frac{x}{5} + \frac{1}{4} = \frac{x}{2} \) by manipulating the equation using operations on rational expressions.

### Step 1: Eliminate the fractions by finding a common denominator
The least common denominator (LCD) for 5, 4, and 2 is 20. Multiply every term by 20 to eliminate the fractions:

\[
20 \cdot \left(\frac{x}{5}\right) + 20 \cdot \left(\frac{1}{4}\right) = 20 \cdot \left(\frac{x}{2}\right)
\]

### Step 2: Simplify each term
\[
4x + 5 = 10x
\]

### Step 3: Solve for \( x \)
To solve for \( x \), first get all terms involving \( x \) on one side of the equation:

\[
4x - 10x = -5
\]

\[
-6x = -5
\]

Now, divide both sides by -6:

\[
x = \frac{5}{6}
\]

So, the solution is \( x = \frac{5}{6} \).

Would you like further details or have any questions?

Here are some related questions:
1. How do you find the least common denominator (LCD)?
2. How do you solve equations with fractions?
3. Can you explain cross-multiplication in rational equations?
4. What are some common mistakes when solving rational equations?
5. How do you check your solution in a rational equation?

**Tip:** Always check your solution by substituting it back into the original equation.

Learn how to solve rational equations with a detailed step-by-step guide. This problem involves manipulating rational expressions and finding common denominators. Suitable for high school students.

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