Evaluate
\frac{x^{5}+2x^{4}+3x^{3}+8x^{2}+4x-5}{x+2}
Differentiate w.r.t. x
\frac{4x^{5}+16x^{4}+22x^{3}+26x^{2}+32x+13}{\left(x+2\right)^{2}}
Graph
Share
Copied to clipboard
\frac{\left(x^{4}+3x^{2}+2x\right)\left(x+2\right)}{x+2}-\frac{5}{x+2}
To add or subtract expressions, expand them to make their denominators the same. Multiply x^{4}+3x^{2}+2x times \frac{x+2}{x+2}.
\frac{\left(x^{4}+3x^{2}+2x\right)\left(x+2\right)-5}{x+2}
Since \frac{\left(x^{4}+3x^{2}+2x\right)\left(x+2\right)}{x+2} and \frac{5}{x+2} have the same denominator, subtract them by subtracting their numerators.
\frac{x^{5}+2x^{4}+3x^{3}+6x^{2}+2x^{2}+4x-5}{x+2}
Do the multiplications in \left(x^{4}+3x^{2}+2x\right)\left(x+2\right)-5.
\frac{x^{5}+2x^{4}+3x^{3}+8x^{2}+4x-5}{x+2}
Combine like terms in x^{5}+2x^{4}+3x^{3}+6x^{2}+2x^{2}+4x-5.
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}