Simplify (7x+8)/(x-7)+(3x)/(7-x)

Problem

(7*x+8)/(x−7)+(3*x)/(7−x)

Solution

1. Identify the denominators in the expression, which are x−7 and 7−x

2. Rewrite the second denominator by factoring out a negative sign so that both fractions have a common denominator: $7-x = -(x-7)$.

3. Adjust the sign of the second fraction using the identity a/(−b)=−a/b

4. Combine the numerators over the common denominator x−7

5. Simplify the numerator by combining like terms: 7*x−3*x+8=4*x+8

Final Answer

(7*x+8)/(x−7)+(3*x)/(7−x)=(4*x+8)/(x−7)

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