https://file.aiquickdraw.com/mathbot/file/1726602916930for5g1cu.jpg

The expression in the image is:

\[
\frac{5x - 1}{4} - \frac{2x - 4}{5}
\]

Let's solve it step by step:

### Step 1: Find a common denominator
The denominators are 4 and 5, so the least common denominator (LCD) is 20. We need to rewrite each fraction with 20 as the denominator.

\[
\frac{5x - 1}{4} = \frac{5(5x - 1)}{20} = \frac{25x - 5}{20}
\]
\[
\frac{2x - 4}{5} = \frac{4(2x - 4)}{20} = \frac{8x - 16}{20}
\]

### Step 2: Rewrite the expression with the common denominator
Now, the expression becomes:

\[
\frac{25x - 5}{20} - \frac{8x - 16}{20}
\]

### Step 3: Combine the fractions
Since both fractions have the same denominator, we can combine the numerators:

\[
\frac{(25x - 5) - (8x - 16)}{20}
\]

Simplify the numerator:

\[
(25x - 5) - (8x - 16) = 25x - 5 - 8x + 16 = 17x + 11
\]

So the expression becomes:

\[
\frac{17x + 11}{20}
\]

### Final Answer:
\[
\frac{17x + 11}{20}
\]

Would you like more details on this solution, or do you have any questions?

Here are 5 related questions to expand on this concept:
1. How do you solve an equation involving similar fractions?
2. How can you find the least common denominator of multiple fractions?
3. What happens if the terms in the numerator are more complex, involving higher powers of \(x\)?
4. Can you solve a similar equation if it’s set equal to zero, such as \(\frac{5x - 1}{4} - \frac{2x - 4}{5} = 0\)?
5. How would this problem change if the subtraction was replaced with addition?

**Tip:** Always remember to simplify the numerators before combining fractions; it makes handling complex expressions easier.

Solve the expression: (5x - 1)/4 - (2x - 4)/5

Learn how to solve the rational expression (5x - 1)/4 - (2x - 4)/5 with detailed steps. This example demonstrates the use of least common denominators and simplification techniques. Suitable for students in Grades 8-10.

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