Solve for x
x=-\frac{y}{y-1}
y\neq 1
Solve for y
y=\frac{x}{x+1}
x\neq -1
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yx+y-x=0
Subtract x from both sides.
yx-x=-y
Subtract y from both sides. Anything subtracted from zero gives its negation.
\left(y-1\right)x=-y
Combine all terms containing x.
\frac{\left(y-1\right)x}{y-1}=-\frac{y}{y-1}
Divide both sides by y-1.
x=-\frac{y}{y-1}
Dividing by y-1 undoes the multiplication by y-1.
\left(x+1\right)y=x
Combine all terms containing y.
\frac{\left(x+1\right)y}{x+1}=\frac{x}{x+1}
Divide both sides by x+1.
y=\frac{x}{x+1}
Dividing by x+1 undoes the multiplication by x+1.
Examples
Quadratic equation
{ 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}