Math, asked by MehtabBhullar, 5 hours ago

solveif x,a,b are not equal to zero

 \frac{1}{a + b + x}  =  \frac{1}{a}  +  \frac{1}{b}  +  \frac{1}{x}

Answers

Answered by shrirampawar249
0

Answer:

 \frac{1}{a + b + x}  =  \frac{1}{a}  +  \frac{1}{b}  +  \frac{1}{x}  \\  \frac{1}{a + b + x}  -  \frac{1}{x}  =  \frac{1}{a}  +  \frac{1}{b}  \\  \frac{x}{x(a + b + x)}  -  \frac{a + b + x}{x(a + b + x)}  =  \frac{b + a}{ab}  \\  \frac{x - a - b - x}{x(a + b + x)}  =  \frac{a + b}{ab}  \\  \frac{ - (a + b)}{x(a + b + x)}  =  \frac{a + b}{ab}  \\  \frac{ - 1}{x(a + b + x)}  =  \frac{1}{ab}  \\  - ab = x(a + b + x) \\  - ab = ax + bx +  {x}^{2}  \\  {x}^{2}  + x(a + b) + ab = 0 \\  {b}^{2}  - 4ac =  {(a + b)}^{2}  - 4(1)(ab) \\   = {a}^{2} +   {b}^{2}  + 2ab - 4ab \\  =  {a}^{2} +   {b}^{2}  - 2ab \\ x =  \frac{ - b +  \sqrt{ {b}^{2}  - 4ac} }{2a}  \\ x =  \frac{ - (a + b) +  \sqrt{ {a}^{2} +  {b}^{2}  -  2ab  } }{2(1)}  \\ x =  \frac{ - a - b + a - b}{2} orx =  \frac{ - a - b - a + b}{2}  \\ x =  \frac{ - 2b}{2} orx =  \frac{ - 2a}{2}  \\ x =  - b \: orx =  - a

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