Evaluate
\frac{44+16x+11x^{2}-x^{3}}{5\left(x^{2}-1\right)}
Expand
-\frac{x^{3}-11x^{2}-16x-44}{5\left(x^{2}-1\right)}
Graph
Share
Copied to clipboard
\frac{2x+1}{x-1}+\frac{8}{\left(x-1\right)\left(x+1\right)}-\frac{x-1}{5}
Factor x^{2}-1.
\frac{\left(2x+1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}+\frac{8}{\left(x-1\right)\left(x+1\right)}-\frac{x-1}{5}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and \left(x-1\right)\left(x+1\right) is \left(x-1\right)\left(x+1\right). Multiply \frac{2x+1}{x-1} times \frac{x+1}{x+1}.
\frac{\left(2x+1\right)\left(x+1\right)+8}{\left(x-1\right)\left(x+1\right)}-\frac{x-1}{5}
Since \frac{\left(2x+1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} and \frac{8}{\left(x-1\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{2x^{2}+2x+x+1+8}{\left(x-1\right)\left(x+1\right)}-\frac{x-1}{5}
Do the multiplications in \left(2x+1\right)\left(x+1\right)+8.
\frac{2x^{2}+3x+9}{\left(x-1\right)\left(x+1\right)}-\frac{x-1}{5}
Combine like terms in 2x^{2}+2x+x+1+8.
\frac{5\left(2x^{2}+3x+9\right)}{5\left(x-1\right)\left(x+1\right)}-\frac{\left(x-1\right)\left(x-1\right)\left(x+1\right)}{5\left(x-1\right)\left(x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-1\right)\left(x+1\right) and 5 is 5\left(x-1\right)\left(x+1\right). Multiply \frac{2x^{2}+3x+9}{\left(x-1\right)\left(x+1\right)} times \frac{5}{5}. Multiply \frac{x-1}{5} times \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}.
\frac{5\left(2x^{2}+3x+9\right)-\left(x-1\right)\left(x-1\right)\left(x+1\right)}{5\left(x-1\right)\left(x+1\right)}
Since \frac{5\left(2x^{2}+3x+9\right)}{5\left(x-1\right)\left(x+1\right)} and \frac{\left(x-1\right)\left(x-1\right)\left(x+1\right)}{5\left(x-1\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{10x^{2}+15x+45-x^{3}+x+x^{2}-1}{5\left(x-1\right)\left(x+1\right)}
Do the multiplications in 5\left(2x^{2}+3x+9\right)-\left(x-1\right)\left(x-1\right)\left(x+1\right).
\frac{11x^{2}+16x+44-x^{3}}{5\left(x-1\right)\left(x+1\right)}
Combine like terms in 10x^{2}+15x+45-x^{3}+x+x^{2}-1.
\frac{11x^{2}+16x+44-x^{3}}{5x^{2}-5}
Expand 5\left(x-1\right)\left(x+1\right).
\frac{2x+1}{x-1}+\frac{8}{\left(x-1\right)\left(x+1\right)}-\frac{x-1}{5}
Factor x^{2}-1.
\frac{\left(2x+1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}+\frac{8}{\left(x-1\right)\left(x+1\right)}-\frac{x-1}{5}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-1 and \left(x-1\right)\left(x+1\right) is \left(x-1\right)\left(x+1\right). Multiply \frac{2x+1}{x-1} times \frac{x+1}{x+1}.
\frac{\left(2x+1\right)\left(x+1\right)+8}{\left(x-1\right)\left(x+1\right)}-\frac{x-1}{5}
Since \frac{\left(2x+1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} and \frac{8}{\left(x-1\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.
\frac{2x^{2}+2x+x+1+8}{\left(x-1\right)\left(x+1\right)}-\frac{x-1}{5}
Do the multiplications in \left(2x+1\right)\left(x+1\right)+8.
\frac{2x^{2}+3x+9}{\left(x-1\right)\left(x+1\right)}-\frac{x-1}{5}
Combine like terms in 2x^{2}+2x+x+1+8.
\frac{5\left(2x^{2}+3x+9\right)}{5\left(x-1\right)\left(x+1\right)}-\frac{\left(x-1\right)\left(x-1\right)\left(x+1\right)}{5\left(x-1\right)\left(x+1\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-1\right)\left(x+1\right) and 5 is 5\left(x-1\right)\left(x+1\right). Multiply \frac{2x^{2}+3x+9}{\left(x-1\right)\left(x+1\right)} times \frac{5}{5}. Multiply \frac{x-1}{5} times \frac{\left(x-1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}.
\frac{5\left(2x^{2}+3x+9\right)-\left(x-1\right)\left(x-1\right)\left(x+1\right)}{5\left(x-1\right)\left(x+1\right)}
Since \frac{5\left(2x^{2}+3x+9\right)}{5\left(x-1\right)\left(x+1\right)} and \frac{\left(x-1\right)\left(x-1\right)\left(x+1\right)}{5\left(x-1\right)\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{10x^{2}+15x+45-x^{3}+x+x^{2}-1}{5\left(x-1\right)\left(x+1\right)}
Do the multiplications in 5\left(2x^{2}+3x+9\right)-\left(x-1\right)\left(x-1\right)\left(x+1\right).
\frac{11x^{2}+16x+44-x^{3}}{5\left(x-1\right)\left(x+1\right)}
Combine like terms in 10x^{2}+15x+45-x^{3}+x+x^{2}-1.
\frac{11x^{2}+16x+44-x^{3}}{5x^{2}-5}
Expand 5\left(x-1\right)\left(x+1\right).
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}