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Question
Simplify:
`(sqrt(x^2 + y^2) - y)/(x - sqrt(x^2 - y^2)) ÷ (sqrt(x^2 - y^2) + x)/(sqrt(x^2 + y^2) + y)`
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Solution
`(sqrt(x^2 + y^2) - y)/(x - sqrt(x^2 - y^2)) ÷ (sqrt(x^2 - y^2) + x)/(sqrt(x^2 + y^2) + y)`
`=> (sqrt(x^2 + y^2) - y)/(x - sqrt(x^2 - y^2)) xx (sqrt(x^2 + y^2) + y)/(sqrt(x^2 - y^2) + x)`
`=> ((sqrt(x^2 + y^2) - y)(sqrt(x^2 + y^2) + y))/((x - sqrt(x^2 - y^2))(x + sqrt(x^2 - y^2)))`
`=> ((sqrt(x^2 + y^2))^2 - y^2)/(x^2 - (sqrt(x^2 - y^2))^2)`
`=> (x^2 + cancel(y^2) - cancel(y^2))/(cancel(x^2) - cancel(x^2) + y^2)`
`=> x^2/y^2`
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