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Solve for x (complex solution)
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Solve for m
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\left(x-1\right)\left(x+1\right)-\left(x+2\right)x=m
Variable x cannot be equal to any of the values -2,1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(x+2\right), the least common multiple of x+2,x-1,x^{2}+x-2.
x^{2}-1-\left(x+2\right)x=m
Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.
x^{2}-1-\left(x^{2}+2x\right)=m
Use the distributive property to multiply x+2 by x.
x^{2}-1-x^{2}-2x=m
To find the opposite of x^{2}+2x, find the opposite of each term.
-1-2x=m
Combine x^{2} and -x^{2} to get 0.
-2x=m+1
Add 1 to both sides.
\frac{-2x}{-2}=\frac{m+1}{-2}
Divide both sides by -2.
x=\frac{m+1}{-2}
Dividing by -2 undoes the multiplication by -2.
x=\frac{-m-1}{2}
Divide m+1 by -2.
x=\frac{-m-1}{2}\text{, }x\neq -2\text{ and }x\neq 1
Variable x cannot be equal to any of the values -2,1.
\left(x-1\right)\left(x+1\right)-\left(x+2\right)x=m
Multiply both sides of the equation by \left(x-1\right)\left(x+2\right), the least common multiple of x+2,x-1,x^{2}+x-2.
x^{2}-1-\left(x+2\right)x=m
Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.
x^{2}-1-\left(x^{2}+2x\right)=m
Use the distributive property to multiply x+2 by x.
x^{2}-1-x^{2}-2x=m
To find the opposite of x^{2}+2x, find the opposite of each term.
-1-2x=m
Combine x^{2} and -x^{2} to get 0.
m=-1-2x
Swap sides so that all variable terms are on the left hand side.
\left(x-1\right)\left(x+1\right)-\left(x+2\right)x=m
Variable x cannot be equal to any of the values -2,1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(x+2\right), the least common multiple of x+2,x-1,x^{2}+x-2.
x^{2}-1-\left(x+2\right)x=m
Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.
x^{2}-1-\left(x^{2}+2x\right)=m
Use the distributive property to multiply x+2 by x.
x^{2}-1-x^{2}-2x=m
To find the opposite of x^{2}+2x, find the opposite of each term.
-1-2x=m
Combine x^{2} and -x^{2} to get 0.
-2x=m+1
Add 1 to both sides.
\frac{-2x}{-2}=\frac{m+1}{-2}
Divide both sides by -2.
x=\frac{m+1}{-2}
Dividing by -2 undoes the multiplication by -2.
x=\frac{-m-1}{2}
Divide m+1 by -2.
x=\frac{-m-1}{2}\text{, }x\neq -2\text{ and }x\neq 1
Variable x cannot be equal to any of the values -2,1.