Solve for k
k=\frac{x+1}{x-3}
x\neq 3
Solve for x
x=\frac{3k+1}{k-1}
k\neq 1
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kx-3k=x+1
Add 1 to both sides.
\left(x-3\right)k=x+1
Combine all terms containing k.
\frac{\left(x-3\right)k}{x-3}=\frac{x+1}{x-3}
Divide both sides by x-3.
k=\frac{x+1}{x-3}
Dividing by x-3 undoes the multiplication by x-3.
kx-3k-1-x=0
Subtract x from both sides.
kx-1-x=3k
Add 3k to both sides. Anything plus zero gives itself.
kx-x=3k+1
Add 1 to both sides.
\left(k-1\right)x=3k+1
Combine all terms containing x.
\frac{\left(k-1\right)x}{k-1}=\frac{3k+1}{k-1}
Divide both sides by k-1.
x=\frac{3k+1}{k-1}
Dividing by k-1 undoes the multiplication by k-1.
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Limits
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