Question

add.
\\(\frac{5x}{2x - 10} + \frac{x - 2}{3x - 15}\\)
simplify your answer as much as possible.

Explanation:

Step1: Factor denominators

Factor \(2x - 10\) as \(2(x - 5)\) and \(3x - 15\) as \(3(x - 5)\). So the expression becomes \(\frac{5x}{2(x - 5)}+\frac{x - 2}{3(x - 5)}\).

Step2: Find common denominator

The common denominator of \(2(x - 5)\) and \(3(x - 5)\) is \(6(x - 5)\). Rewrite each fraction with the common denominator: \(\frac{5x\times3}{6(x - 5)}+\frac{(x - 2)\times2}{6(x - 5)}=\frac{15x}{6(x - 5)}+\frac{2x - 4}{6(x - 5)}\).

Step3: Add the numerators

Add the numerators over the common denominator: \(\frac{15x+2x - 4}{6(x - 5)}=\frac{17x - 4}{6(x - 5)}\).

Answer:

\(\frac{17x - 4}{6(x - 5)}\)