Add and simplify: \( \frac{8}{x+8}+\frac{x+136}{x^{2}-64} \) \( \square \)
Real Tutor Solution
Answer
Solution
Reviewed and approved by the UpStudy tutoring team
Explain 
Simplify this solution Mind Expander
To simplify \( \frac{8}{x+8}+\frac{x+136}{x^{2}-64} \), we first notice that \( x^2 - 64 \) can be factored as \( (x-8)(x+8) \). Now, rewrite the expression: \[ \frac{8}{x+8} + \frac{x+136}{(x-8)(x+8)} \] Next, we need a common denominator, which is \( (x-8)(x+8) \). We can rewrite the first term: \[ \frac{8(x-8)}{(x-8)(x+8)} \] So now our expression looks like this: \[ \frac{8(x-8) + (x+136)}{(x-8)(x+8)} \] Now, simplify the numerator: \[ 8(x - 8) + (x + 136) = 8x - 64 + x + 136 = 9x + 72 \] Putting it back together, we get: \[ \frac{9x + 72}{(x-8)(x+8)} \] Now we can factor out a 9 from the numerator: \[ \frac{9(x + 8)}{(x-8)(x+8)} \] The \( x + 8 \) terms cancel out (assuming \( x \neq -8 \)): \[ \frac{9}{x-8} \] Thus, the simplified expression is: \[ \frac{9}{x-8} \]
