Solve for v
v=-\frac{\sqrt{x+2}+\sqrt{3x-5}+3\sqrt{2x-5}-7\sqrt{2}-2}{x}
x\geq \frac{5}{2}
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vx+\sqrt{3x-5}+\sqrt{x+2}+3\sqrt{2x-5}=7\sqrt{2}+2
Add 2 to both sides.
vx+\sqrt{x+2}+3\sqrt{2x-5}=7\sqrt{2}+2-\sqrt{3x-5}
Subtract \sqrt{3x-5} from both sides.
vx+3\sqrt{2x-5}=7\sqrt{2}+2-\sqrt{3x-5}-\sqrt{x+2}
Subtract \sqrt{x+2} from both sides.
vx=7\sqrt{2}+2-\sqrt{3x-5}-\sqrt{x+2}-3\sqrt{2x-5}
Subtract 3\sqrt{2x-5} from both sides.
xv=-\sqrt{x+2}-\sqrt{3x-5}-3\sqrt{2x-5}+7\sqrt{2}+2
The equation is in standard form.
\frac{xv}{x}=\frac{-\sqrt{x+2}-\sqrt{3x-5}-3\sqrt{2x-5}+7\sqrt{2}+2}{x}
Divide both sides by x.
v=\frac{-\sqrt{x+2}-\sqrt{3x-5}-3\sqrt{2x-5}+7\sqrt{2}+2}{x}
Dividing by x undoes the multiplication by x.
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