Solve for a
a=5+\frac{1}{x}
x\neq 0
Solve for x
x=\frac{1}{a-5}
a\neq 5
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ax=5x+1
Add 1 to both sides.
xa=5x+1
The equation is in standard form.
\frac{xa}{x}=\frac{5x+1}{x}
Divide both sides by x.
a=\frac{5x+1}{x}
Dividing by x undoes the multiplication by x.
a=5+\frac{1}{x}
Divide 5x+1 by x.
ax-1-5x=0
Subtract 5x from both sides.
ax-5x=1
Add 1 to both sides. Anything plus zero gives itself.
\left(a-5\right)x=1
Combine all terms containing x.
\frac{\left(a-5\right)x}{a-5}=\frac{1}{a-5}
Divide both sides by a-5.
x=\frac{1}{a-5}
Dividing by a-5 undoes the multiplication by a-5.
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
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Matrix
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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}