Question

add.
\\(\frac{2}{x - 4} + \frac{3}{5x}\\)
simplify your answer as much as possible.

Explanation:

Step1: Find the common denominator

The denominators are \(x - 4\) and \(5x\). The common denominator is \(5x(x - 4)\).
Multiply the first fraction by \(\frac{5x}{5x}\) and the second fraction by \(\frac{x - 4}{x - 4}\):
\(\frac{2}{x - 4} \times \frac{5x}{5x}=\frac{10x}{5x(x - 4)}\)
\(\frac{3}{5x} \times \frac{x - 4}{x - 4}=\frac{3(x - 4)}{5x(x - 4)}\)

Step2: Add the fractions

Now that the fractions have the same denominator, add the numerators:
\(\frac{10x + 3(x - 4)}{5x(x - 4)}\)

Step3: Simplify the numerator

Expand and combine like terms in the numerator:
\(10x+3x - 12 = 13x - 12\)

Answer:

\(\frac{13x - 12}{5x(x - 4)}\)