Evaluate
\frac{1}{b^{2}+1}
Expand
\frac{1}{b^{2}+1}
Share
Copied to clipboard
\frac{b^{2}+2}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)}+\frac{3}{\left(b-1\right)\left(b+1\right)\left(-b^{2}-1\right)}
Factor b^{4}-1. Factor 1-b^{4}.
\frac{b^{2}+2}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)}+\frac{3\left(-1\right)}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(b-1\right)\left(b+1\right)\left(b^{2}+1\right) and \left(b-1\right)\left(b+1\right)\left(-b^{2}-1\right) is \left(b-1\right)\left(b+1\right)\left(b^{2}+1\right). Multiply \frac{3}{\left(b-1\right)\left(b+1\right)\left(-b^{2}-1\right)} times \frac{-1}{-1}.
\frac{b^{2}+2+3\left(-1\right)}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)}
Since \frac{b^{2}+2}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)} and \frac{3\left(-1\right)}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)} have the same denominator, add them by adding their numerators.
\frac{b^{2}+2-3}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)}
Do the multiplications in b^{2}+2+3\left(-1\right).
\frac{b^{2}-1}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)}
Combine like terms in b^{2}+2-3.
\frac{\left(b-1\right)\left(b+1\right)}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)}
Factor the expressions that are not already factored in \frac{b^{2}-1}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)}.
\frac{1}{b^{2}+1}
Cancel out \left(b-1\right)\left(b+1\right) in both numerator and denominator.
\frac{b^{2}+2}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)}+\frac{3}{\left(b-1\right)\left(b+1\right)\left(-b^{2}-1\right)}
Factor b^{4}-1. Factor 1-b^{4}.
\frac{b^{2}+2}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)}+\frac{3\left(-1\right)}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(b-1\right)\left(b+1\right)\left(b^{2}+1\right) and \left(b-1\right)\left(b+1\right)\left(-b^{2}-1\right) is \left(b-1\right)\left(b+1\right)\left(b^{2}+1\right). Multiply \frac{3}{\left(b-1\right)\left(b+1\right)\left(-b^{2}-1\right)} times \frac{-1}{-1}.
\frac{b^{2}+2+3\left(-1\right)}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)}
Since \frac{b^{2}+2}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)} and \frac{3\left(-1\right)}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)} have the same denominator, add them by adding their numerators.
\frac{b^{2}+2-3}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)}
Do the multiplications in b^{2}+2+3\left(-1\right).
\frac{b^{2}-1}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)}
Combine like terms in b^{2}+2-3.
\frac{\left(b-1\right)\left(b+1\right)}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)}
Factor the expressions that are not already factored in \frac{b^{2}-1}{\left(b-1\right)\left(b+1\right)\left(b^{2}+1\right)}.
\frac{1}{b^{2}+1}
Cancel out \left(b-1\right)\left(b+1\right) in both numerator and denominator.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}