Solve for x
x=-\frac{4y}{y+1}
y\neq -1
Solve for y
y=-\frac{x}{x+4}
x\neq -4
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-4y-xy-x=0
Swap sides so that all variable terms are on the left hand side.
-xy-x=4y
Add 4y to both sides. Anything plus zero gives itself.
\left(-y-1\right)x=4y
Combine all terms containing x.
\frac{\left(-y-1\right)x}{-y-1}=\frac{4y}{-y-1}
Divide both sides by -y-1.
x=\frac{4y}{-y-1}
Dividing by -y-1 undoes the multiplication by -y-1.
x=-\frac{4y}{y+1}
Divide 4y by -y-1.
-4y-xy-x=0
Swap sides so that all variable terms are on the left hand side.
-4y-xy=x
Add x to both sides. Anything plus zero gives itself.
\left(-4-x\right)y=x
Combine all terms containing y.
\left(-x-4\right)y=x
The equation is in standard form.
\frac{\left(-x-4\right)y}{-x-4}=\frac{x}{-x-4}
Divide both sides by -4-x.
y=\frac{x}{-x-4}
Dividing by -4-x undoes the multiplication by -4-x.
y=-\frac{x}{x+4}
Divide x by -4-x.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}