Solve for m (complex solution)
\left\{\begin{matrix}m=\frac{x+2y+3}{x+y+3}\text{, }&x\neq -\left(y+3\right)\\m\in \mathrm{C}\text{, }&x=-3\text{ and }y=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=-\frac{my-2y+3m-3}{m-1}\text{, }&m\neq 1\\x\in \mathrm{C}\text{, }&y=0\text{ and }m=1\end{matrix}\right.
Solve for m
\left\{\begin{matrix}m=\frac{x+2y+3}{x+y+3}\text{, }&x\neq -\left(y+3\right)\\m\in \mathrm{R}\text{, }&x=-3\text{ and }y=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=-\frac{my-2y+3m-3}{m-1}\text{, }&m\neq 1\\x\in \mathrm{R}\text{, }&y=0\text{ and }m=1\end{matrix}\right.
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mx-x+\left(m-2\right)y+3m-3=0
Use the distributive property to multiply m-1 by x.
mx-x+my-2y+3m-3=0
Use the distributive property to multiply m-2 by y.
mx+my-2y+3m-3=x
Add x to both sides. Anything plus zero gives itself.
mx+my+3m-3=x+2y
Add 2y to both sides.
mx+my+3m=x+2y+3
Add 3 to both sides.
\left(x+y+3\right)m=x+2y+3
Combine all terms containing m.
\frac{\left(x+y+3\right)m}{x+y+3}=\frac{x+2y+3}{x+y+3}
Divide both sides by x+y+3.
m=\frac{x+2y+3}{x+y+3}
Dividing by x+y+3 undoes the multiplication by x+y+3.
mx-x+\left(m-2\right)y+3m-3=0
Use the distributive property to multiply m-1 by x.
mx-x+my-2y+3m-3=0
Use the distributive property to multiply m-2 by y.
mx-x-2y+3m-3=-my
Subtract my from both sides. Anything subtracted from zero gives its negation.
mx-x+3m-3=-my+2y
Add 2y to both sides.
mx-x-3=-my+2y-3m
Subtract 3m from both sides.
mx-x=-my+2y-3m+3
Add 3 to both sides.
\left(m-1\right)x=-my+2y-3m+3
Combine all terms containing x.
\left(m-1\right)x=3-3m+2y-my
The equation is in standard form.
\frac{\left(m-1\right)x}{m-1}=\frac{3-3m+2y-my}{m-1}
Divide both sides by m-1.
x=\frac{3-3m+2y-my}{m-1}
Dividing by m-1 undoes the multiplication by m-1.
mx-x+\left(m-2\right)y+3m-3=0
Use the distributive property to multiply m-1 by x.
mx-x+my-2y+3m-3=0
Use the distributive property to multiply m-2 by y.
mx+my-2y+3m-3=x
Add x to both sides. Anything plus zero gives itself.
mx+my+3m-3=x+2y
Add 2y to both sides.
mx+my+3m=x+2y+3
Add 3 to both sides.
\left(x+y+3\right)m=x+2y+3
Combine all terms containing m.
\frac{\left(x+y+3\right)m}{x+y+3}=\frac{x+2y+3}{x+y+3}
Divide both sides by x+y+3.
m=\frac{x+2y+3}{x+y+3}
Dividing by x+y+3 undoes the multiplication by x+y+3.
mx-x+\left(m-2\right)y+3m-3=0
Use the distributive property to multiply m-1 by x.
mx-x+my-2y+3m-3=0
Use the distributive property to multiply m-2 by y.
mx-x-2y+3m-3=-my
Subtract my from both sides. Anything subtracted from zero gives its negation.
mx-x+3m-3=-my+2y
Add 2y to both sides.
mx-x-3=-my+2y-3m
Subtract 3m from both sides.
mx-x=-my+2y-3m+3
Add 3 to both sides.
\left(m-1\right)x=-my+2y-3m+3
Combine all terms containing x.
\left(m-1\right)x=3-3m+2y-my
The equation is in standard form.
\frac{\left(m-1\right)x}{m-1}=\frac{3-3m+2y-my}{m-1}
Divide both sides by m-1.
x=\frac{3-3m+2y-my}{m-1}
Dividing by m-1 undoes the multiplication by m-1.
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Integration
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Limits
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