Solve for a
a=\frac{3\left(x+5\right)}{5f\left(x-2\right)}
x\neq 2\text{ and }f\neq 0\text{ and }x\neq -5
Solve for f
f=\frac{3\left(x+5\right)}{5a\left(x-2\right)}
x\neq 2\text{ and }a\neq 0\text{ and }x\neq -5
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5\left(x-2\right)fa=3\left(x+5\right)
Multiply both sides of the equation by 5\left(x+5\right), the least common multiple of x+5,5.
\left(5x-10\right)fa=3\left(x+5\right)
Use the distributive property to multiply 5 by x-2.
\left(5xf-10f\right)a=3\left(x+5\right)
Use the distributive property to multiply 5x-10 by f.
5xfa-10fa=3\left(x+5\right)
Use the distributive property to multiply 5xf-10f by a.
5xfa-10fa=3x+15
Use the distributive property to multiply 3 by x+5.
\left(5xf-10f\right)a=3x+15
Combine all terms containing a.
\left(5fx-10f\right)a=3x+15
The equation is in standard form.
\frac{\left(5fx-10f\right)a}{5fx-10f}=\frac{3x+15}{5fx-10f}
Divide both sides by 5fx-10f.
a=\frac{3x+15}{5fx-10f}
Dividing by 5fx-10f undoes the multiplication by 5fx-10f.
a=\frac{3\left(x+5\right)}{5f\left(x-2\right)}
Divide 15+3x by 5fx-10f.
5\left(x-2\right)fa=3\left(x+5\right)
Multiply both sides of the equation by 5\left(x+5\right), the least common multiple of x+5,5.
\left(5x-10\right)fa=3\left(x+5\right)
Use the distributive property to multiply 5 by x-2.
\left(5xf-10f\right)a=3\left(x+5\right)
Use the distributive property to multiply 5x-10 by f.
5xfa-10fa=3\left(x+5\right)
Use the distributive property to multiply 5xf-10f by a.
5xfa-10fa=3x+15
Use the distributive property to multiply 3 by x+5.
\left(5xa-10a\right)f=3x+15
Combine all terms containing f.
\left(5ax-10a\right)f=3x+15
The equation is in standard form.
\frac{\left(5ax-10a\right)f}{5ax-10a}=\frac{3x+15}{5ax-10a}
Divide both sides by 5ax-10a.
f=\frac{3x+15}{5ax-10a}
Dividing by 5ax-10a undoes the multiplication by 5ax-10a.
f=\frac{3\left(x+5\right)}{5a\left(x-2\right)}
Divide 15+3x by 5ax-10a.
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}