Solve for f
f=-\frac{5}{-x+y-3}
y\neq x+3
Solve for x
x=y-3+\frac{5}{f}
f\neq 0
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fy=fx+3f-5
Use the distributive property to multiply f by x+3.
fy-fx=3f-5
Subtract fx from both sides.
fy-fx-3f=-5
Subtract 3f from both sides.
\left(y-x-3\right)f=-5
Combine all terms containing f.
\left(-x+y-3\right)f=-5
The equation is in standard form.
\frac{\left(-x+y-3\right)f}{-x+y-3}=-\frac{5}{-x+y-3}
Divide both sides by y-x-3.
f=-\frac{5}{-x+y-3}
Dividing by y-x-3 undoes the multiplication by y-x-3.
fy=fx+3f-5
Use the distributive property to multiply f by x+3.
fx+3f-5=fy
Swap sides so that all variable terms are on the left hand side.
fx-5=fy-3f
Subtract 3f from both sides.
fx=fy-3f+5
Add 5 to both sides.
\frac{fx}{f}=\frac{fy-3f+5}{f}
Divide both sides by f.
x=\frac{fy-3f+5}{f}
Dividing by f undoes the multiplication by f.
x=y-3+\frac{5}{f}
Divide fy-3f+5 by f.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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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}