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Add.
The numerator should be expanded and simplified. The denominator should be either expanded or factored.

(4)/(x+7)+(8)/(x-1)=

Add.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline4x+7+8x1= \frac{4}{x+7}+\frac{8}{x-1}=

Full solution

Q. Add.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline4x+7+8x1= \frac{4}{x+7}+\frac{8}{x-1}=
  1. Find Common Denominator: To add the two fractions, we need a common denominator. The common denominators for (x+7)(x+7) and (x1)(x-1) would be the product of the two, which is (x+7)(x1)(x+7)(x-1).
  2. Rewrite with Common Denominator: We rewrite each fraction with the common denominator: 4x+7x1x1+8x1x+7x+7\frac{4}{x+7} \cdot \frac{x-1}{x-1} + \frac{8}{x-1} \cdot \frac{x+7}{x+7}
  3. Distribute Numerators: Now we distribute the numerators:\newline(4(x1))/((x+7)(x1))+(8(x+7))/((x+7)(x1))(4 \cdot (x-1)) / ((x+7)(x-1)) + (8 \cdot (x+7)) / ((x+7)(x-1))
  4. Expand Numerators: We expand the numerators: (4x4)/((x+7)(x1))+(8x+56)/((x+7)(x1))(4x - 4) / ((x+7)(x-1)) + (8x + 56) / ((x+7)(x-1))
  5. Combine Numerators: Now we combine the numerators over the common denominator: \newlineegin{equation}\newline\frac{(44x - 44 + 88x + 5656)}{(x+77)(x1-1)}\newline\end{equation}
  6. Simplify Numerator: We simplify the numerator by combining like terms: \newline(12x+52)/((x+7)(x1))(12x + 52) / ((x+7)(x-1))
  7. Final Answer: The numerator is already simplified, and the denominator is already factored. So, we have our final answer: \newline(12x+52)/((x+7)(x1))(12x + 52) / ((x+7)(x-1))