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Question
Make y the subject of the formula x = `(1 - y^2)/(1 + y^2)`. Find y if x = `(3)/(5)`
Solution
x = `(1 - y^2)/(1 + y^2)`
⇒ x (1 + y2) = 1 - y2
⇒ x + y2 = 1 - y2
⇒ xy2 + y2 = 1 - x
⇒ y2 (x + 1) = 1 - x
⇒ y2 = `(1 - x)/(1 + x)`
⇒ y = `sqrt((1 - x)/(1 + x)`
Substituting x = `(3)/(5)`, we get
y = `sqrt((1 - 3/5)/(1 + 3/5)`
= `sqrt(2/8)`
= `sqrt(1/4)`
= `(1)/(2)`.
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