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Square both sides of the equation to remove the square root.

Biology

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Answer

U=C2b−aC2−1U = \frac{C^2b - a}{C^2 - 1}

Step-by-step solution

6 steps

  1. Square both sides of the equation to remove the square root.

    C=U−aU−bC = \sqrt{\frac{U-a}{U-b}} C2=(U−aU−b)2C^2 = \left(\sqrt{\frac{U-a}{U-b}}\right)^2 C2=U−aU−bC^2 = \frac{U-a}{U-b}

  2. Multiply both sides by (U−b)(U-b) to eliminate the denominator.

    C2(U−b)=U−aC^2(U-b) = U-a

  3. Expand the left side of the equation.

    C2U−C2b=U−aC^2U - C^2b = U-a

  4. Collect all terms containing UU on one side and terms not containing UU on the other side.

    Subtract UU from both sides and add C2bC^2b to both sides.

    C2U−U=C2b−aC^2U - U = C^2b - a

  5. Factor out UU from the terms on the left side.

    U(C2−1)=C2b−aU(C^2 - 1) = C^2b - a

  6. Divide both sides by (C2−1)(C^2 - 1) to isolate UU.

    U=C2b−aC2−1U = \frac{C^2b - a}{C^2 - 1}
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