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