Prove that: x⁻¹/(x⁻¹ + y⁻¹) + x⁻¹/(x⁻¹ - y⁻¹) = 2y²/(y² - x²)
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LHS = x⁻¹/(x⁻¹ + y⁻¹) + x⁻¹/(x⁻¹ - y⁻¹)
= 1/x / (1/x+1/y) + 1/x / (1/x-1/y)
solving
= y / y+x + y / y-x
= (y-x)y + (y+x)y / y^2 -xy +xy -x^2
= 2y^2 / y^2 - x^2
= RHS
= 1/x / (1/x+1/y) + 1/x / (1/x-1/y)
solving
= y / y+x + y / y-x
= (y-x)y + (y+x)y / y^2 -xy +xy -x^2
= 2y^2 / y^2 - x^2
= RHS
rudeawakening:
your welcome!!
yup you are correct!
Then how will it equal RHS?
RHS is 2y^2/ (y^2 - x^2) which we get on solving LHS
LHS = RHS
i am getting 2y^2 / (x^2 - y^2) on solving LHS
i know what u have done
while taking lcm u might have replaced x and y's position
Ooops, did a silly error, lol Thanks for your help!
yeah you r welcome
Answered by
0
Answer:
Show that x-¹+y-¹x¹-y-¹ x² + y²
x-1
xy
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