Solve for x
x=\frac{3\left(y+1\right)}{2y-1}
y\neq \frac{1}{2}
Solve for y
y=\frac{x+3}{2x-3}
x\neq \frac{3}{2}
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2xy-x-3=3y
Add 3y to both sides. Anything plus zero gives itself.
2xy-x=3y+3
Add 3 to both sides.
\left(2y-1\right)x=3y+3
Combine all terms containing x.
\frac{\left(2y-1\right)x}{2y-1}=\frac{3y+3}{2y-1}
Divide both sides by 2y-1.
x=\frac{3y+3}{2y-1}
Dividing by 2y-1 undoes the multiplication by 2y-1.
x=\frac{3\left(y+1\right)}{2y-1}
Divide 3+3y by 2y-1.
2xy-3y-3=x
Add x to both sides. Anything plus zero gives itself.
2xy-3y=x+3
Add 3 to both sides.
\left(2x-3\right)y=x+3
Combine all terms containing y.
\frac{\left(2x-3\right)y}{2x-3}=\frac{x+3}{2x-3}
Divide both sides by 2x-3.
y=\frac{x+3}{2x-3}
Dividing by 2x-3 undoes the multiplication by 2x-3.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}