Question

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

Explanation:

Step1: Factor denominators

$\frac{5x}{2(x+5)} + \frac{x-2}{3(x+5)}$

Step2: Find common denominator

Common denominator is $6(x+5)$

Step3: Rewrite fractions

$\frac{5x \cdot 3}{6(x+5)} + \frac{(x-2) \cdot 2}{6(x+5)}$

Step4: Expand numerators

$\frac{15x}{6(x+5)} + \frac{2x-4}{6(x+5)}$

Step5: Combine fractions

$\frac{15x + 2x - 4}{6(x+5)}$

Step6: Simplify numerator

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

Answer:

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