Question

simplify the function algebraically and find the limit
lim_{x
ightarrow5}\frac{x^{2}+2x - 35}{x^{2}-10x + 25}
simplify the given limit.
lim_{x
ightarrow5}\frac{x^{2}+2x - 35}{x^{2}-10x + 25}=lim_{x
ightarrow5}(square)
(type an expression using x as the variable. simplify your answer.)

Explanation:

Step1: Factor numerator and denominator

$x^2 + 2x - 35=(x + 7)(x - 5)$ and $x^2-10x + 25=(x - 5)^2$. So, $\lim_{x
ightarrow5}\frac{x^2 + 2x - 35}{x^2-10x + 25}=\lim_{x
ightarrow5}\frac{(x + 7)(x - 5)}{(x - 5)^2}$.

Step2: Simplify the function

Cancel out common factor $(x - 5)$ (for $x
eq5$), we get $\lim_{x
ightarrow5}\frac{x + 7}{x - 5}$.

Answer:

$\lim_{x
ightarrow5}\frac{x + 7}{x - 5}$