Q. Add.The numerator should be expanded and simplified. The denominator should be either expanded or factored.x+74+x−18=
Find Common Denominator: To add the two fractions, we need a common denominator. The common denominators for (x+7) and (x−1) would be the product of the two, which is (x+7)(x−1).
Rewrite with Common Denominator: We rewrite each fraction with the common denominator: x+74⋅x−1x−1+x−18⋅x+7x+7
Distribute Numerators: Now we distribute the numerators:(4⋅(x−1))/((x+7)(x−1))+(8⋅(x+7))/((x+7)(x−1))
Expand Numerators: We expand the numerators: (4x−4)/((x+7)(x−1))+(8x+56)/((x+7)(x−1))
Combine Numerators: Now we combine the numerators over the common denominator: egin{equation}\frac{(4x - 4 + 8x + 56)}{(x+7)(x−1)}\end{equation}
Simplify Numerator: We simplify the numerator by combining like terms: (12x+52)/((x+7)(x−1))
Final Answer: The numerator is already simplified, and the denominator is already factored. So, we have our final answer: (12x+52)/((x+7)(x−1))
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