Solve for f (complex solution)
\left\{\begin{matrix}f=\frac{y+4}{x+5}\text{, }&x\neq -5\\f\in \mathrm{C}\text{, }&y=-4\text{ and }x=-5\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=\frac{y-5f+4}{f}\text{, }&f\neq 0\\x\in \mathrm{C}\text{, }&y=-4\text{ and }f=0\end{matrix}\right.
Solve for f
\left\{\begin{matrix}f=\frac{y+4}{x+5}\text{, }&x\neq -5\\f\in \mathrm{R}\text{, }&y=-4\text{ and }x=-5\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{y-5f+4}{f}\text{, }&f\neq 0\\x\in \mathrm{R}\text{, }&y=-4\text{ and }f=0\end{matrix}\right.
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y=fx+5f-4
Use the distributive property to multiply f by x+5.
fx+5f-4=y
Swap sides so that all variable terms are on the left hand side.
fx+5f=y+4
Add 4 to both sides.
\left(x+5\right)f=y+4
Combine all terms containing f.
\frac{\left(x+5\right)f}{x+5}=\frac{y+4}{x+5}
Divide both sides by x+5.
f=\frac{y+4}{x+5}
Dividing by x+5 undoes the multiplication by x+5.
y=fx+5f-4
Use the distributive property to multiply f by x+5.
fx+5f-4=y
Swap sides so that all variable terms are on the left hand side.
fx-4=y-5f
Subtract 5f from both sides.
fx=y-5f+4
Add 4 to both sides.
\frac{fx}{f}=\frac{y-5f+4}{f}
Divide both sides by f.
x=\frac{y-5f+4}{f}
Dividing by f undoes the multiplication by f.
y=fx+5f-4
Use the distributive property to multiply f by x+5.
fx+5f-4=y
Swap sides so that all variable terms are on the left hand side.
fx+5f=y+4
Add 4 to both sides.
\left(x+5\right)f=y+4
Combine all terms containing f.
\frac{\left(x+5\right)f}{x+5}=\frac{y+4}{x+5}
Divide both sides by x+5.
f=\frac{y+4}{x+5}
Dividing by x+5 undoes the multiplication by x+5.
y=fx+5f-4
Use the distributive property to multiply f by x+5.
fx+5f-4=y
Swap sides so that all variable terms are on the left hand side.
fx-4=y-5f
Subtract 5f from both sides.
fx=y-5f+4
Add 4 to both sides.
\frac{fx}{f}=\frac{y-5f+4}{f}
Divide both sides by f.
x=\frac{y-5f+4}{f}
Dividing by f undoes the multiplication by f.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
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}