Questions: This question: 2 point(s) possible Add and, if possible, simplify. [ (a-5b)/(a+b)+(a+7b)/(a+b) ] (a-5b)/(a+b)+(a+7b)/(a+b)= (Simplify your answer. Type an integer or a fraction.)

Solution Steps

To add the given fractions, we first observe that they have the same denominator. This allows us to directly add the numerators while keeping the common denominator. After adding the numerators, we simplify the resulting expression if possible.

We start with the expression: \[ \frac{a - 5b}{a + b} + \frac{a + 7b}{a + b} \] Since both fractions have the same denominator, we can combine the numerators: \[ \frac{(a - 5b) + (a + 7b)}{a + b} \]

Next, we simplify the numerator: \[ (a - 5b) + (a + 7b) = a - 5b + a + 7b = 2a + 2b \] Thus, the expression becomes: \[ \frac{2a + 2b}{a + b} \]

We can factor out a 2 from the numerator: \[ \frac{2(a + b)}{a + b} \] Since \(a + b\) is common in both the numerator and the denominator, we can cancel it out (assuming \(a + b \neq 0\)): \[ 2 \]

Final Answer