(35sqrt(x ^ 2 + 10x + 25))/(x + 5) ,но x > - 5

To simplify the expression \(\frac{35\sqrt{x^2 + 10x + 25}}{x + 5}\) given that \(x > -5\), we start by simplifying the expression under the square root. First, observe that: \[ x^2 + 10x + 25 = (x + 5)^2 \] Thus, we can rewrite the expression: \[ \sqrt{x^2 + 10x + 25} = \sqrt{(x + 5)^2} \] Since \(x > -5\), \(\sqrt{(x + 5)^2} = x + 5\). Now replace \(\sqrt{x^2 + 10x + 25}\) in the original expression: \[ \frac{35\sqrt{x^2 + 10x + 25}}{x + 5} = \frac{35(x + 5)}{x + 5} \] Since \(x + 5\) is on both the numerator and the denominator (and not equal to zero when \(x > -5\)), we can simplify this to: \[ 35 \] So, the simplified expression is: \[ \boxed{35} \] for \(x > -5\).