Solve for y
y=-x-3+\frac{5}{x}
x\neq 0
Solve for x
x=\frac{\sqrt{y^{2}+6y+29}-y-3}{2}
x=\frac{-\sqrt{y^{2}+6y+29}-y-3}{2}
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3x+xy=5-x^{2}
Subtract x^{2} from both sides.
xy=5-x^{2}-3x
Subtract 3x from both sides.
xy=5-3x-x^{2}
The equation is in standard form.
\frac{xy}{x}=\frac{5-3x-x^{2}}{x}
Divide both sides by x.
y=\frac{5-3x-x^{2}}{x}
Dividing by x undoes the multiplication by x.
y=-x-3+\frac{5}{x}
Divide 5-x^{2}-3x by x.
Examples
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{ 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}