Solve for x
x=\frac{y}{1-4y}
y\neq \frac{1}{4}
Solve for y
y=\frac{x}{4x+1}
x\neq -\frac{1}{4}
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x-y-4xy=0
Subtract 4xy from both sides.
x-4xy=y
Add y to both sides. Anything plus zero gives itself.
\left(1-4y\right)x=y
Combine all terms containing x.
\frac{\left(1-4y\right)x}{1-4y}=\frac{y}{1-4y}
Divide both sides by 1-4y.
x=\frac{y}{1-4y}
Dividing by 1-4y undoes the multiplication by 1-4y.
x-y-4xy=0
Subtract 4xy from both sides.
-y-4xy=-x
Subtract x from both sides. Anything subtracted from zero gives its negation.
\left(-1-4x\right)y=-x
Combine all terms containing y.
\left(-4x-1\right)y=-x
The equation is in standard form.
\frac{\left(-4x-1\right)y}{-4x-1}=-\frac{x}{-4x-1}
Divide both sides by -1-4x.
y=-\frac{x}{-4x-1}
Dividing by -1-4x undoes the multiplication by -1-4x.
y=\frac{x}{4x+1}
Divide -x by -1-4x.
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}