Solve for f
f=\frac{x}{3}
x\neq -1
Solve for x
x=3f
f\neq -\frac{1}{3}
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x\left(x+1\right)=f\left(3x+3\right)
Multiply both sides of the equation by x+1.
x^{2}+x=f\left(3x+3\right)
Use the distributive property to multiply x by x+1.
x^{2}+x=3fx+3f
Use the distributive property to multiply f by 3x+3.
3fx+3f=x^{2}+x
Swap sides so that all variable terms are on the left hand side.
\left(3x+3\right)f=x^{2}+x
Combine all terms containing f.
\frac{\left(3x+3\right)f}{3x+3}=\frac{x\left(x+1\right)}{3x+3}
Divide both sides by 3x+3.
f=\frac{x\left(x+1\right)}{3x+3}
Dividing by 3x+3 undoes the multiplication by 3x+3.
f=\frac{x}{3}
Divide x\left(1+x\right) by 3x+3.
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