Solve for y
y=\sqrt{x}+\frac{1}{x}
x>0
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1+x\sqrt{x}=yx
Multiply both sides of the equation by x.
yx=1+x\sqrt{x}
Swap sides so that all variable terms are on the left hand side.
xy=\sqrt{x}x+1
The equation is in standard form.
\frac{xy}{x}=\frac{x^{\frac{3}{2}}+1}{x}
Divide both sides by x.
y=\frac{x^{\frac{3}{2}}+1}{x}
Dividing by x undoes the multiplication by x.
y=\sqrt{x}+\frac{1}{x}
Divide x^{\frac{3}{2}}+1 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
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