Question

solve for x : 1/a+b+c-1/x=1/a+1/b​

Answer 1

Answer:

$x = -a \text{ and } y = -b$

Step-by-step explanation:

$\cfrac{1}{a+b+x}-\cfrac{1}{x} = \cfrac{1}{a}+\cfrac{1}{b}$

$\Rightarrow \cfrac{x-a-b-x}{(a+b+x)(x)} = \cfrac{b+a}{ab}$

$\Rightarrow \cfrac{-a-b}{ax+bx+x^2}=\cfrac{a+b}{ab}$

$\Rightarrow -\cfrac{a+b}{ax+bx+x^2}=\cfrac{a+b}{ab}$

$\Rightarrow -\cfrac{1}{ax+bx+x^2} = \cfrac{1}{ab}$

$\Rightarrow ax+bx+x^2=-ab$

$\Rightarrow x^2+ax+bx+ab=0$

$\Rightarrow x(x+a)+b(x+a)=0$

$\Rightarrow (x+a)(x+b)=0$

$\therefore x=-a \text{ and } y=-b$

Please mark my answer as BRAINLIEST.