Evaluate
15x^{3}-5x-6+\frac{2}{x^{2}}
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15x^{3}-5x-6+\frac{2}{x^{2}}
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5x^{3}\left(-x^{-2}\right)+15x^{3}-2\left(-x^{-2}\right)-6
Use the distributive property to multiply 5x^{3}-2 by -x^{-2}+3.
5x^{3}\left(-x^{-2}\right)+15x^{3}+2x^{-2}-6
Multiply -2 and -1 to get 2.
-5x^{3}x^{-2}+15x^{3}+2x^{-2}-6
Multiply 5 and -1 to get -5.
-5x^{1}+15x^{3}+2x^{-2}-6
To multiply powers of the same base, add their exponents. Add 3 and -2 to get 1.
-5x+15x^{3}+2x^{-2}-6
Calculate x to the power of 1 and get x.
5x^{3}\left(-x^{-2}\right)+15x^{3}-2\left(-x^{-2}\right)-6
Use the distributive property to multiply 5x^{3}-2 by -x^{-2}+3.
5x^{3}\left(-x^{-2}\right)+15x^{3}+2x^{-2}-6
Multiply -2 and -1 to get 2.
-5x^{3}x^{-2}+15x^{3}+2x^{-2}-6
Multiply 5 and -1 to get -5.
-5x^{1}+15x^{3}+2x^{-2}-6
To multiply powers of the same base, add their exponents. Add 3 and -2 to get 1.
-5x+15x^{3}+2x^{-2}-6
Calculate x to the power of 1 and get x.
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}