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Question
\frac{\left(x^{3}+x^{2}+x+2\right)}{\left(x^{2}-1\right)}
Simplify the expression
\frac{x^{3}+x^{2}+x+2}{x^{2}-1}
Evaluate
\frac{\left(x^{3}+x^{2}+x+2\right)}{\left(x^{2}-1\right)}
Solution
\frac{x^{3}+x^{2}+x+2}{x^{2}-1}
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Find the excluded values
x=1,x=-1
Evaluate
\frac{\left(x^{3}+x^{2}+x+2\right)}{\left(x^{2}-1\right)}
To find the excluded values,set the denominators equal to 0
x^{2}-1=0
Move the constant to the right-hand side and change its sign
x^{2}=0+1
Removing 0 doesn't change the value,so remove it from the expression
x^{2}=1
Take the root of both sides of the equation and remember to use both positive and negative roots
x=\pm \sqrt{1}
Simplify the expression
x=\pm 1
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=1\\&x=-1\end{align}
Solution
x=1,x=-1
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Divide the polynomials
x+1+\frac{2x+3}{x^{2}-1}
Evaluate
\frac{\left(x^{3}+x^{2}+x+2\right)}{\left(x^{2}-1\right)}
Solution
x+1+\frac{2x+3}{x^{2}-1}
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Find the roots
x\approx -1.35321
Evaluate
\frac{\left(x^{3}+x^{2}+x+2\right)}{\left(x^{2}-1\right)}
To find the roots of the expression,set the expression equal to 0
\frac{\left(x^{3}+x^{2}+x+2\right)}{\left(x^{2}-1\right)}=0
Find the domain
More Steps
Evaluate
x^{2}-1\neq 0
Move the constant to the right side
x^{2}\neq 1
Take the root of both sides of the equation and remember to use both positive and negative roots
x\neq \pm \sqrt{1}
Simplify the expression
x\neq \pm 1
\text{Separate the inequality into }2\text{ possible cases}
\left\{ \begin{array}{l}x\neq 1\\x\neq -1\end{array}\right.
Find the intersection
x \in \left(-\infty,-1\right)\cup \left(-1,1\right)\cup \left(1,+\infty\right)
\frac{\left(x^{3}+x^{2}+x+2\right)}{\left(x^{2}-1\right)}=0,x \in \left(-\infty,-1\right)\cup \left(-1,1\right)\cup \left(1,+\infty\right)
Calculate
\frac{\left(x^{3}+x^{2}+x+2\right)}{\left(x^{2}-1\right)}=0
Remove the parentheses
\frac{x^{3}+x^{2}+x+2}{\left(x^{2}-1\right)}=0
Remove the parentheses
\frac{x^{3}+x^{2}+x+2}{x^{2}-1}=0
Cross multiply
x^{3}+x^{2}+x+2=\left(x^{2}-1\right)\times 0
Simplify the equation
x^{3}+x^{2}+x+2=0
Calculate
x\approx -1.35321
Check if the solution is in the defined range
x\approx -1.35321,x \in \left(-\infty,-1\right)\cup \left(-1,1\right)\cup \left(1,+\infty\right)
Solution
x\approx -1.35321
Show Solutions
