Solve for a
a=b+\frac{1}{x}
x\neq 0
Solve for b
b=a-\frac{1}{x}
x\neq 0
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ax=bx+1
Add 1 to both sides.
xa=bx+1
The equation is in standard form.
\frac{xa}{x}=\frac{bx+1}{x}
Divide both sides by x.
a=\frac{bx+1}{x}
Dividing by x undoes the multiplication by x.
a=b+\frac{1}{x}
Divide bx+1 by x.
bx=ax-1
Swap sides so that all variable terms are on the left hand side.
xb=ax-1
The equation is in standard form.
\frac{xb}{x}=\frac{ax-1}{x}
Divide both sides by x.
b=\frac{ax-1}{x}
Dividing by x undoes the multiplication by x.
b=a-\frac{1}{x}
Divide ax-1 by x.
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Limits
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