Add. The numerator should be expanded and simplified. The denominator should be either expanded or factored. (8x)/(x^(2)-49)+(5)/(x^(2)-4x-21)=

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Add. The numerator should be expanded and simplified. The denominator should be either expanded or factored.  (8x)/(x^(2)-49)+(5)/(x^(2)-4x-21)=

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Factor Denominators: First, we need to factor the denominators of both fractions to see if they can be simplified or if there are common factors that will help us combine the fractions. The first denominator is x^2 - 49, which is a difference of squares and can be factored as (x + 7)(x - 7). The second denominator is x^2 - 4x - 21, which is a quadratic expression that can be factored. We look for two numbers that multiply to -21 and add up to -4. These numbers are -7 and +3. So, the factored form of the second denominator is (x - 7)(x + 3).Write Expression with Factors: Now that we have factored both denominators, we can write the expression with these factors: (8x)/((x + 7)(x - 7)) + (5)/((x - 7)(x + 3))Find Least Common Denominator: To add these fractions, we need a common denominator. The least common denominator (LCD) is the product of the distinct factors from both denominators, which is (x + 7)(x - 7)(x + 3).Adjust Fractions for LCD: We will rewrite each fraction with the LCD as the denominator. For the first fraction, we already have (x + 7)(x - 7) in the denominator, so we need to multiply the numerator and denominator by (x + 3) to get the LCD. For the second fraction, we need to multiply the numerator and denominator by (x + 7).Combine Fractions with LCD: After adjusting the fractions to have the LCD, we get: (8x * (x + 3))/((x + 7)(x - 7)(x + 3)) + (5 * (x + 7))/((x - 7)(x + 3)(x + 7))Expand Numerators: Now we can combine the fractions since they have the same denominator: (8x * (x + 3) + 5 * (x + 7))/((x + 7)(x - 7)(x + 3))Combine Like Terms: Next, we expand the numerators of both terms: (8x^2 + 24x + 5x + 35)/((x + 7)(x - 7)(x + 3))Final Answer: Combine like terms in the numerator: (8x^2 + 29x + 35)/((x + 7)(x - 7)(x + 3))The numerator is fully expanded and simplified, and the denominator is already factored. So, the final answer is: (8x^2 + 29x + 35)/((x + 7)(x - 7)(x + 3))

Add. $\newline$ The numerator should be expanded and simplified. The denominator should be either expanded or factored. $\newline$ $\frac{8 x}{x^{2}-49}+\frac{5}{x^{2}-4 x-21}=$

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Add.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline8xx2−49+5x2−4x−21= \frac{8 x}{x^{2}-49}+\frac{5}{x^{2}-4 x-21}= x2−498x​+x2−4x−215​=

Add. $\newline$ The numerator should be expanded and simplified. The denominator should be either expanded or factored. $\newline$ $\frac{8 x}{x^{2}-49}+\frac{5}{x^{2}-4 x-21}=$