Solve for a
a=\frac{x^{3}+bx+2}{x^{2}}
x\neq 0
Solve for b
b=ax-x^{2}-\frac{2}{x}
x\neq 0
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x^{3}-ax^{2}+2=-bx
Subtract bx from both sides. Anything subtracted from zero gives its negation.
x^{3}-ax^{2}=-bx-2
Subtract 2 from both sides.
-ax^{2}=-bx-2-x^{3}
Subtract x^{3} from both sides.
\left(-x^{2}\right)a=-x^{3}-bx-2
The equation is in standard form.
\frac{\left(-x^{2}\right)a}{-x^{2}}=\frac{-x^{3}-bx-2}{-x^{2}}
Divide both sides by -x^{2}.
a=\frac{-x^{3}-bx-2}{-x^{2}}
Dividing by -x^{2} undoes the multiplication by -x^{2}.
a=\frac{bx+2}{x^{2}}+x
Divide -bx-2-x^{3} by -x^{2}.
bx+2=-\left(x^{3}-ax^{2}\right)
Subtract x^{3}-ax^{2} from both sides. Anything subtracted from zero gives its negation.
bx=-\left(x^{3}-ax^{2}\right)-2
Subtract 2 from both sides.
bx=-x^{3}+ax^{2}-2
To find the opposite of x^{3}-ax^{2}, find the opposite of each term.
xb=-x^{3}+ax^{2}-2
The equation is in standard form.
\frac{xb}{x}=\frac{-x^{3}+ax^{2}-2}{x}
Divide both sides by x.
b=\frac{-x^{3}+ax^{2}-2}{x}
Dividing by x undoes the multiplication by x.
b=ax-x^{2}-\frac{2}{x}
Divide -x^{3}+ax^{2}-2 by x.
Examples
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y = 3x + 4
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Matrix
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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
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