Solve for y (complex solution)
\left\{\begin{matrix}y=0\text{, }&x\neq -1\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\neq -1\text{, }&y=0\end{matrix}\right.
Solve for y
\left\{\begin{matrix}y=0\text{, }&x\neq -1\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
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y=\frac{xy}{1+x}+\frac{y\left(1+x\right)}{1+x}
To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{1+x}{1+x}.
y=\frac{xy+y\left(1+x\right)}{1+x}
Since \frac{xy}{1+x} and \frac{y\left(1+x\right)}{1+x} have the same denominator, add them by adding their numerators.
y=\frac{xy+y+xy}{1+x}
Do the multiplications in xy+y\left(1+x\right).
y=\frac{2xy+y}{1+x}
Combine like terms in xy+y+xy.
y-\frac{2xy+y}{1+x}=0
Subtract \frac{2xy+y}{1+x} from both sides.
\frac{y\left(1+x\right)}{1+x}-\frac{2xy+y}{1+x}=0
To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{1+x}{1+x}.
\frac{y\left(1+x\right)-\left(2xy+y\right)}{1+x}=0
Since \frac{y\left(1+x\right)}{1+x} and \frac{2xy+y}{1+x} have the same denominator, subtract them by subtracting their numerators.
\frac{y+xy-2yx-y}{1+x}=0
Do the multiplications in y\left(1+x\right)-\left(2xy+y\right).
\frac{-xy}{1+x}=0
Combine like terms in y+xy-2yx-y.
-xy=0
Multiply both sides of the equation by x+1.
\left(-x\right)y=0
The equation is in standard form.
y=0
Divide 0 by -x.
y\left(x+1\right)=xy+\left(x+1\right)y
Variable x cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by x+1.
yx+y=xy+\left(x+1\right)y
Use the distributive property to multiply y by x+1.
yx+y=xy+xy+y
Use the distributive property to multiply x+1 by y.
yx+y=2xy+y
Combine xy and xy to get 2xy.
yx+y-2xy=y
Subtract 2xy from both sides.
-yx+y=y
Combine yx and -2xy to get -yx.
-yx=y-y
Subtract y from both sides.
-yx=0
Combine y and -y to get 0.
\left(-y\right)x=0
The equation is in standard form.
x=0
Divide 0 by -y.
y=\frac{xy}{1+x}+\frac{y\left(1+x\right)}{1+x}
To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{1+x}{1+x}.
y=\frac{xy+y\left(1+x\right)}{1+x}
Since \frac{xy}{1+x} and \frac{y\left(1+x\right)}{1+x} have the same denominator, add them by adding their numerators.
y=\frac{xy+y+xy}{1+x}
Do the multiplications in xy+y\left(1+x\right).
y=\frac{2xy+y}{1+x}
Combine like terms in xy+y+xy.
y-\frac{2xy+y}{1+x}=0
Subtract \frac{2xy+y}{1+x} from both sides.
\frac{y\left(1+x\right)}{1+x}-\frac{2xy+y}{1+x}=0
To add or subtract expressions, expand them to make their denominators the same. Multiply y times \frac{1+x}{1+x}.
\frac{y\left(1+x\right)-\left(2xy+y\right)}{1+x}=0
Since \frac{y\left(1+x\right)}{1+x} and \frac{2xy+y}{1+x} have the same denominator, subtract them by subtracting their numerators.
\frac{y+xy-2yx-y}{1+x}=0
Do the multiplications in y\left(1+x\right)-\left(2xy+y\right).
\frac{-xy}{1+x}=0
Combine like terms in y+xy-2yx-y.
-xy=0
Multiply both sides of the equation by x+1.
\left(-x\right)y=0
The equation is in standard form.
y=0
Divide 0 by -x.
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}