Evaluate
-\frac{10\left(x+2\right)x^{2}}{x-7}
Expand
-\frac{10\left(x^{3}+2x^{2}\right)}{x-7}
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\frac{\left(10x^{3}+20x^{2}\right)\left(42+x-x^{2}\right)}{\left(x-7\right)\left(x^{2}-x-42\right)}
Divide \frac{10x^{3}+20x^{2}}{x-7} by \frac{x^{2}-x-42}{42+x-x^{2}} by multiplying \frac{10x^{3}+20x^{2}}{x-7} by the reciprocal of \frac{x^{2}-x-42}{42+x-x^{2}}.
\frac{-\left(x^{2}-x-42\right)\left(10x^{3}+20x^{2}\right)}{\left(x-7\right)\left(x^{2}-x-42\right)}
Extract the negative sign in 42+x-x^{2}.
\frac{-\left(10x^{3}+20x^{2}\right)}{x-7}
Cancel out x^{2}-x-42 in both numerator and denominator.
\frac{-10x^{3}-20x^{2}}{x-7}
To find the opposite of 10x^{3}+20x^{2}, find the opposite of each term.
\frac{\left(10x^{3}+20x^{2}\right)\left(42+x-x^{2}\right)}{\left(x-7\right)\left(x^{2}-x-42\right)}
Divide \frac{10x^{3}+20x^{2}}{x-7} by \frac{x^{2}-x-42}{42+x-x^{2}} by multiplying \frac{10x^{3}+20x^{2}}{x-7} by the reciprocal of \frac{x^{2}-x-42}{42+x-x^{2}}.
\frac{-\left(x^{2}-x-42\right)\left(10x^{3}+20x^{2}\right)}{\left(x-7\right)\left(x^{2}-x-42\right)}
Extract the negative sign in 42+x-x^{2}.
\frac{-\left(10x^{3}+20x^{2}\right)}{x-7}
Cancel out x^{2}-x-42 in both numerator and denominator.
\frac{-10x^{3}-20x^{2}}{x-7}
To find the opposite of 10x^{3}+20x^{2}, find the opposite of each term.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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y = 3x + 4
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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}