Questions: Find the sum of these rational expressions. 4/(x-6) + 8/(x+3) (?x+□)/((x-6)(x+3))

Solution Steps

To find the sum of the given rational expressions, we need to find a common denominator, which is the product of the individual denominators \((x-6)\) and \((x+3)\). Then, we rewrite each fraction with this common denominator and add the numerators.

To add the rational expressions \(\frac{4}{x-6}\) and \(\frac{8}{x+3}\), we first identify the common denominator, which is the product of the individual denominators: \((x-6)(x+3)\).

Rewrite each fraction with the common denominator:

• \(\frac{4}{x-6} = \frac{4(x+3)}{(x-6)(x+3)}\)
• \(\frac{8}{x+3} = \frac{8(x-6)}{(x-6)(x+3)}\)

Add the numerators of the rewritten fractions: \[ \frac{4(x+3) + 8(x-6)}{(x-6)(x+3)} = \frac{4x + 12 + 8x - 48}{(x-6)(x+3)} \]

Combine like terms in the numerator: \[ \frac{12x - 36}{(x-6)(x+3)} \]

Factor out the common factor in the numerator: \[ \frac{12(x - 3)}{(x-6)(x+3)} \]

Final Answer