Question

add.
\\(\frac{x+6}{4x-8} + \frac{x+2}{5x-10}\\)
simplify your answer as much as possible.

Explanation:

Step1: Factor denominators

Factor \(4x - 8\) as \(4(x - 2)\) and \(5x - 10\) as \(5(x - 2)\). So the expression becomes \(\frac{x + 6}{4(x - 2)}+\frac{x + 2}{5(x - 2)}\).

Step2: Find common denominator

The common denominator of \(4(x - 2)\) and \(5(x - 2)\) is \(20(x - 2)\). Rewrite each fraction with the common denominator: \(\frac{(x + 6)\times5}{20(x - 2)}+\frac{(x + 2)\times4}{20(x - 2)}\).

Step3: Expand numerators

Expand the numerators: \(\frac{5x+30}{20(x - 2)}+\frac{4x + 8}{20(x - 2)}\).

Step4: Add numerators

Add the numerators: \(\frac{5x + 30+4x + 8}{20(x - 2)}\).

Step5: Combine like terms

Combine like terms in the numerator: \(\frac{9x+38}{20(x - 2)}\).

Answer:

\(\frac{9x + 38}{20(x - 2)}\)