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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-2xy-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-2xy-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.