x(r+s)=1

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Solution for x(r+s)=1 equation: 


Simplifying
x(r + s) = 1
(r * x + s * x) = 1
(rx + sx) = 1

Solving
rx + sx = 1

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '-1sx' to each side of the equation.
rx + sx + -1sx = 1 + -1sx

Combine like terms: sx + -1sx = 0
rx + 0 = 1 + -1sx
rx = 1 + -1sx

Divide each side by 'x'.
r = x-1 + -1s

Simplifying
r = x-1 + -1s

Reorder the terms:
r = -1s + x-1

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