Solve for A (complex solution)
\left\{\begin{matrix}A=\frac{y\left(1-x\right)^{2}}{v\left(2x+3\right)}\text{, }&x\neq -\frac{3}{2}\text{ and }v\neq 0\text{ and }x\neq 1\\A\in \mathrm{C}\text{, }&\left(x=-\frac{3}{2}\text{ or }v=0\right)\text{ and }y=0\text{ and }x\neq 1\end{matrix}\right.
Solve for v (complex solution)
\left\{\begin{matrix}v=\frac{y\left(1-x\right)^{2}}{A\left(2x+3\right)}\text{, }&x\neq -\frac{3}{2}\text{ and }A\neq 0\text{ and }x\neq 1\\v\in \mathrm{C}\text{, }&\left(x=-\frac{3}{2}\text{ or }A=0\right)\text{ and }y=0\text{ and }x\neq 1\end{matrix}\right.
Solve for A
\left\{\begin{matrix}A=\frac{y\left(1-x\right)^{2}}{v\left(2x+3\right)}\text{, }&x\neq -\frac{3}{2}\text{ and }v\neq 0\text{ and }x\neq 1\\A\in \mathrm{R}\text{, }&\left(x=-\frac{3}{2}\text{ or }v=0\right)\text{ and }y=0\text{ and }x\neq 1\end{matrix}\right.
Solve for v
\left\{\begin{matrix}v=\frac{y\left(1-x\right)^{2}}{A\left(2x+3\right)}\text{, }&x\neq -\frac{3}{2}\text{ and }A\neq 0\text{ and }x\neq 1\\v\in \mathrm{R}\text{, }&\left(x=-\frac{3}{2}\text{ or }A=0\right)\text{ and }y=0\text{ and }x\neq 1\end{matrix}\right.
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Linear Equation
5 problems similar to:
y = \frac { 2 x + 3 } { x - 1 } \quad \frac { A v } { x - 1 }
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y\left(x-1\right)=\left(2x+3\right)\times \frac{Av}{x-1}
Multiply both sides of the equation by x-1.
yx-y=\left(2x+3\right)\times \frac{Av}{x-1}
Use the distributive property to multiply y by x-1.
yx-y=\frac{\left(2x+3\right)Av}{x-1}
Express \left(2x+3\right)\times \frac{Av}{x-1} as a single fraction.
yx-y=\frac{\left(2xA+3A\right)v}{x-1}
Use the distributive property to multiply 2x+3 by A.
yx-y=\frac{2xAv+3Av}{x-1}
Use the distributive property to multiply 2xA+3A by v.
\frac{2xAv+3Av}{x-1}=yx-y
Swap sides so that all variable terms are on the left hand side.
2xAv+3Av=yx\left(x-1\right)-y\left(x-1\right)
Multiply both sides of the equation by x-1.
2xAv+3Av=yx^{2}-yx-y\left(x-1\right)
Use the distributive property to multiply yx by x-1.
2xAv+3Av=yx^{2}-yx-yx+y
Use the distributive property to multiply -y by x-1.
2xAv+3Av=yx^{2}-2yx+y
Combine -yx and -yx to get -2yx.
\left(2xv+3v\right)A=yx^{2}-2yx+y
Combine all terms containing A.
\left(2vx+3v\right)A=y+yx^{2}-2xy
The equation is in standard form.
\frac{\left(2vx+3v\right)A}{2vx+3v}=\frac{y\left(x-1\right)^{2}}{2vx+3v}
Divide both sides by 2vx+3v.
A=\frac{y\left(x-1\right)^{2}}{2vx+3v}
Dividing by 2vx+3v undoes the multiplication by 2vx+3v.
A=\frac{y\left(x-1\right)^{2}}{v\left(2x+3\right)}
Divide y\left(-1+x\right)^{2} by 2vx+3v.
y\left(x-1\right)=\left(2x+3\right)\times \frac{Av}{x-1}
Multiply both sides of the equation by x-1.
yx-y=\left(2x+3\right)\times \frac{Av}{x-1}
Use the distributive property to multiply y by x-1.
yx-y=\frac{\left(2x+3\right)Av}{x-1}
Express \left(2x+3\right)\times \frac{Av}{x-1} as a single fraction.
yx-y=\frac{\left(2xA+3A\right)v}{x-1}
Use the distributive property to multiply 2x+3 by A.
yx-y=\frac{2xAv+3Av}{x-1}
Use the distributive property to multiply 2xA+3A by v.
\frac{2xAv+3Av}{x-1}=yx-y
Swap sides so that all variable terms are on the left hand side.
2xAv+3Av=yx\left(x-1\right)-y\left(x-1\right)
Multiply both sides of the equation by x-1.
2xAv+3Av=yx^{2}-yx-y\left(x-1\right)
Use the distributive property to multiply yx by x-1.
2xAv+3Av=yx^{2}-yx-yx+y
Use the distributive property to multiply -y by x-1.
2xAv+3Av=yx^{2}-2yx+y
Combine -yx and -yx to get -2yx.
\left(2xA+3A\right)v=yx^{2}-2yx+y
Combine all terms containing v.
\left(2Ax+3A\right)v=y+yx^{2}-2xy
The equation is in standard form.
\frac{\left(2Ax+3A\right)v}{2Ax+3A}=\frac{y\left(x-1\right)^{2}}{2Ax+3A}
Divide both sides by 2Ax+3A.
v=\frac{y\left(x-1\right)^{2}}{2Ax+3A}
Dividing by 2Ax+3A undoes the multiplication by 2Ax+3A.
v=\frac{y\left(x-1\right)^{2}}{A\left(2x+3\right)}
Divide y\left(-1+x\right)^{2} by 2Ax+3A.
y\left(x-1\right)=\left(2x+3\right)\times \frac{Av}{x-1}
Multiply both sides of the equation by x-1.
yx-y=\left(2x+3\right)\times \frac{Av}{x-1}
Use the distributive property to multiply y by x-1.
yx-y=\frac{\left(2x+3\right)Av}{x-1}
Express \left(2x+3\right)\times \frac{Av}{x-1} as a single fraction.
yx-y=\frac{\left(2xA+3A\right)v}{x-1}
Use the distributive property to multiply 2x+3 by A.
yx-y=\frac{2xAv+3Av}{x-1}
Use the distributive property to multiply 2xA+3A by v.
\frac{2xAv+3Av}{x-1}=yx-y
Swap sides so that all variable terms are on the left hand side.
2xAv+3Av=yx\left(x-1\right)-y\left(x-1\right)
Multiply both sides of the equation by x-1.
2xAv+3Av=yx^{2}-yx-y\left(x-1\right)
Use the distributive property to multiply yx by x-1.
2xAv+3Av=yx^{2}-yx-yx+y
Use the distributive property to multiply -y by x-1.
2xAv+3Av=yx^{2}-2yx+y
Combine -yx and -yx to get -2yx.
\left(2xv+3v\right)A=yx^{2}-2yx+y
Combine all terms containing A.
\left(2vx+3v\right)A=y+yx^{2}-2xy
The equation is in standard form.
\frac{\left(2vx+3v\right)A}{2vx+3v}=\frac{y\left(x-1\right)^{2}}{2vx+3v}
Divide both sides by 2vx+3v.
A=\frac{y\left(x-1\right)^{2}}{2vx+3v}
Dividing by 2vx+3v undoes the multiplication by 2vx+3v.
A=\frac{y\left(x-1\right)^{2}}{v\left(2x+3\right)}
Divide y\left(-1+x\right)^{2} by 2vx+3v.
y\left(x-1\right)=\left(2x+3\right)\times \frac{Av}{x-1}
Multiply both sides of the equation by x-1.
yx-y=\left(2x+3\right)\times \frac{Av}{x-1}
Use the distributive property to multiply y by x-1.
yx-y=\frac{\left(2x+3\right)Av}{x-1}
Express \left(2x+3\right)\times \frac{Av}{x-1} as a single fraction.
yx-y=\frac{\left(2xA+3A\right)v}{x-1}
Use the distributive property to multiply 2x+3 by A.
yx-y=\frac{2xAv+3Av}{x-1}
Use the distributive property to multiply 2xA+3A by v.
\frac{2xAv+3Av}{x-1}=yx-y
Swap sides so that all variable terms are on the left hand side.
2xAv+3Av=yx\left(x-1\right)-y\left(x-1\right)
Multiply both sides of the equation by x-1.
2xAv+3Av=yx^{2}-yx-y\left(x-1\right)
Use the distributive property to multiply yx by x-1.
2xAv+3Av=yx^{2}-yx-yx+y
Use the distributive property to multiply -y by x-1.
2xAv+3Av=yx^{2}-2yx+y
Combine -yx and -yx to get -2yx.
\left(2xA+3A\right)v=yx^{2}-2yx+y
Combine all terms containing v.
\left(2Ax+3A\right)v=y+yx^{2}-2xy
The equation is in standard form.
\frac{\left(2Ax+3A\right)v}{2Ax+3A}=\frac{y\left(x-1\right)^{2}}{2Ax+3A}
Divide both sides by 2Ax+3A.
v=\frac{y\left(x-1\right)^{2}}{2Ax+3A}
Dividing by 2Ax+3A undoes the multiplication by 2Ax+3A.
v=\frac{y\left(x-1\right)^{2}}{A\left(2x+3\right)}
Divide y\left(-1+x\right)^{2} by 2Ax+3A.
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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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}