4. Solve $$ V \sqrt{U}=2 \sqrt{U+1} $$ to find $$ U $$ in terms of $$ V $$.

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Solve the equation $$ V \sqrt{U}=2 \sqrt{U+1} $$.
Solve the equation by following steps:
- step0: Solve for $$U$$:
  $$V\sqrt{U}=2\sqrt{U+1}$$
- step1: Rewrite the expression:
  $$\sqrt{U}=\frac{2\sqrt{U+1}}{V}$$
- step2: Raise both sides to the $$2$$-th power$$:$$
  $$\left(\sqrt{U}\right)^{2}=\left(\frac{2\sqrt{U+1}}{V}\right)^{2}$$
- step3: Evaluate the power:
  $$U=\frac{4U+4}{V^{2}}$$
- step4: Cross multiply:
  $$UV^{2}=4U+4$$
- step5: Simplify the equation:
  $$V^{2}U=4U+4$$
- step6: Move the variable to the left side:
  $$V^{2}U-4U=4$$
- step7: Collect like terms:
  $$\left(V^{2}-4\right)U=4$$
- step8: Divide both sides:
  $$\frac{\left(V^{2}-4\right)U}{V^{2}-4}=\frac{4}{V^{2}-4}$$
- step9: Divide the numbers:
  $$U=\frac{4}{V^{2}-4}$$
The solution to the equation $$ V \sqrt{U}=2 \sqrt{U+1} $$ is $$ U=\frac{4}{V^{2}-4} $$.
$$ U=\frac{4}{V^{2}-4} $$

Solve to find in terms of .

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