Advertisements
Advertisements
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)`
Advertisements
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`
APPEARS IN
RELATED QUESTIONS
Rationalise the denominators of : `3/sqrt5`
Rationalise the denominators of : `(2sqrt3)/sqrt5`
Rationalise the denominators of:
`[sqrt6 - sqrt5]/[sqrt6 + sqrt5]`
Simplify by rationalising the denominator in the following.
`(5sqrt(3) - sqrt(15))/(5sqrt(3) + sqrt(15)`
Simplify by rationalising the denominator in the following.
`(7sqrt(3) - 5sqrt(2))/(sqrt(48) + sqrt(18)`
Simplify the following :
`(6)/(2sqrt(3) - sqrt(6)) + sqrt(6)/(sqrt(3) + sqrt(2)) - (4sqrt(3))/(sqrt(6) - sqrt(2)`
Simplify the following :
`(4sqrt(3))/((2 - sqrt(2))) - (30)/((4sqrt(3) - 3sqrt(2))) - (3sqrt(2))/((3 + 2sqrt(3))`
If x = `(7 + 4sqrt(3))`, find the value of
`sqrt(x) + (1)/(sqrt(x)`
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) - 1)`, find the values of
x2 - y2 + xy
Show that: `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + (2 sqrt3)/(sqrt3 - sqrt2) = 11`
