Final Answer
$\frac{\left(x+3\right)\left(x-4\right)}{x+2}$
Got another answer? Verify it here!
Step-by-step Solution
Specify the solving method
Choose an option Simplify Factor Factor by completing the square Find the integral Find the derivative Find the derivative using the definition Solve by quadratic formula (general formula) Find the roots Find break even points Find the discriminant Suggest another method or feature
Send
Intermediate steps
1
Simplify the fraction $\frac{\frac{x^2-16}{x-1}}{\frac{x^2+6x+8}{x^2+2x-3}}$
$\frac{\left(x^2-16\right)\left(x^2+2x-3\right)}{\left(x-1\right)\left(x^2+6x+8\right)}$
Explain this step further
2
Factor the trinomial $\left(x^2+2x-3\right)$ finding two numbers that multiply to form $-3$ and added form $2$
$\begin{matrix}\left(-1\right)\left(3\right)=-3\\ \left(-1\right)+\left(3\right)=2\end{matrix}$
$\frac{\left(x^2-16\right)\left(x-1\right)\left(x+3\right)}{\left(x-1\right)\left(x^2+6x+8\right)}$
4
Factor the trinomial $\left(x^2+6x+8\right)$ finding two numbers that multiply to form $8$ and added form $6$
$\begin{matrix}\left(2\right)\left(4\right)=8\\ \left(2\right)+\left(4\right)=6\end{matrix}$
$\frac{\left(x^2-16\right)\left(x-1\right)\left(x+3\right)}{\left(x-1\right)\left(x+2\right)\left(x+4\right)}$
$\frac{\left(x^2-16\right)\left(x+3\right)}{\left(x+2\right)\left(x+4\right)}$
Intermediate steps
7
Factor the difference of squares $\left(x^2-16\right)$ as the product of two conjugated binomials
$\frac{\left(x+4\right)\left(x+3\right)\left(x-4\right)}{\left(x+2\right)\left(x+4\right)}$
Explain this step further
$\frac{\left(x+3\right)\left(x-4\right)}{x+2}$
Final Answer
$\frac{\left(x+3\right)\left(x-4\right)}{x+2}$