Here, we show you a step-by-step solved example of limits by factoring. This solution was automatically generated by our smart calculator:
Factor the trinomial $x^2+2x-24$ finding two numbers that multiply to form $-24$ and added form $2$
Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values
Simplify $\sqrt{x^2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $\frac{1}{2}$
Calculate the power $\sqrt{16}$
Simplify $\sqrt{x^2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $\frac{1}{2}$
Calculate the power $\sqrt{16}$
Multiply $-1$ times $4$
Factor the difference of squares $x^2-16$ as the product of two conjugated binomials
Simplify the fraction $\frac{\left(x+4\right)\left(x-4\right)}{\left(x-4\right)\left(x+6\right)}$ by $x-4$
Evaluate the limit $\lim_{x\to4}\left(\frac{x+4}{x+6}\right)$ by replacing all occurrences of $x$ by $4$
Add the values $4$ and $6$
Add the values $4$ and $4$
Divide $8$ by $10$
Evaluate the limit $\lim_{x\to4}\left(\frac{x+4}{x+6}\right)$ by replacing all occurrences of $x$ by $4$
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