Solve for x
x=\sqrt{15}+4\approx 7.872983346
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\sqrt{5}x-\sqrt{5}=\sqrt{3}\left(x+1\right)
Use the distributive property to multiply \sqrt{5} by x-1.
\sqrt{5}x-\sqrt{5}=\sqrt{3}x+\sqrt{3}
Use the distributive property to multiply \sqrt{3} by x+1.
\sqrt{5}x-\sqrt{5}-\sqrt{3}x=\sqrt{3}
Subtract \sqrt{3}x from both sides.
\sqrt{5}x-\sqrt{3}x=\sqrt{3}+\sqrt{5}
Add \sqrt{5} to both sides.
\left(\sqrt{5}-\sqrt{3}\right)x=\sqrt{3}+\sqrt{5}
Combine all terms containing x.
\frac{\left(\sqrt{5}-\sqrt{3}\right)x}{\sqrt{5}-\sqrt{3}}=\frac{\sqrt{3}+\sqrt{5}}{\sqrt{5}-\sqrt{3}}
Divide both sides by \sqrt{5}-\sqrt{3}.
x=\frac{\sqrt{3}+\sqrt{5}}{\sqrt{5}-\sqrt{3}}
Dividing by \sqrt{5}-\sqrt{3} undoes the multiplication by \sqrt{5}-\sqrt{3}.
x=\sqrt{15}+4
Divide \sqrt{3}+\sqrt{5} by \sqrt{5}-\sqrt{3}.
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