Make x the subject in the following relations. 1. t = sqrt((x-a)/(x-b))

Question

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Step 1: Square both sides of the equation to eliminate the square root. t = √((x−a)/(x−b)); t² = (√((x−a)/(x−b)))²; t² = (x−a)/(x−b) Step 2: Multiply both sides by (x−b) to remove the fraction. t²(x−b) = x−a Step 3: Expand the left side of the equation. t²x − t²b = x−a Step 4: Collect all terms containing x on one side and terms without x on the other side. t²x − x = t²b − a Step 5: Factor out x from the terms on the left side. x(t² − 1) = t²b − a Step 6: Divide both sides by (t² − 1) to isolate x. x = (t²b − a)/(t² − 1); The final answer is x = (t²b − a)/(t² − 1).

Make x the subject in the following relations. 1. t = sqrt((x−a)/(x-b))

Answer

Step-by-step solution

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

Multiply both sides by $(x-b)$ to remove the fraction.

Expand the left side of the equation.

Collect all terms containing $x$ on one side and terms without $x$ on the other side.

Factor out $x$ from the terms on the left side.

Divide both sides by $(t^2 - 1)$ to isolate $x$ .

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