Question

find x: 1/a+b+x = 1/a + 1/b + 1/x​

Answer 1

Solution -

$\sf{ \dfrac{ 1 }{ a + b + x } = \dfrac{ 1}{a} + \dfrac{1}{b} + \dfrac{1}{x} } \\ \\ \sf{ \implies { \dfrac{ 1 }{ a + b + x } - \dfrac{ 1}{x} = \dfrac{ 1 }{ a } + \dfrac{ 1 }{ b } }} \\ \\ \sf{ \implies { \dfrac{x - a - b - x }{ ( a + b + x ) x } = \dfrac{ a + b }{ ab } }} \\ \\ \sf{ \implies { \dfrac{ -a - b } { ( a + b + x ) x } = \dfrac{ a + b }{ ab } }} \\ \\ \sf{ \implies { \dfrac{ -1 }{( a + b + x ) x } = \dfrac{ 1 }{ ab } }} \\ \\ \sf{ \bold { Cross \: Multiplying \: - }} \\ \\ \sf{ a + b + x = - ab } \\ \\ \sf{ \implies { x = \dfrac{ - ab }{ a + b } }} \\ \\ \sf{ \bold { This \: is \: the \: required \: answer \: . }}$

__________________________________________________

Answer 2

$\huge\underline{\underline{\mathfrak{\color{teal} Solution:}}}$

$\rule{300}{2}$

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

$\bold{\implies \frac{1}{a + b + x} - \frac{1}{x} = \frac{1}{a} + \frac{1}{b} }$

$\bold{\implies \frac{\cancel{x} - a - b - \cancel{ x}}{(a + b + x)x} = \frac{a + b}{ab} }$

$\bold{\implies \frac{ - a - b}{(a + b + x)x} = \frac{a + b}{ab} }$

$\bold{\implies \frac{ - 1}{(a + b + x)x} = \frac{1}{ab} }$

$\sf{Now ,\: by \: cross \: multiplying \: ,we \: get,}$

$\bold{\implies( a + b + x)x = - ab}$

$\bold{\implies x = \frac{ - ab}{a + b + x} }$

$\sf{Therefore ,\: thehe \: required \: value \: of \: x = \frac{ - ab}{a + b + x} }$

$\rule{300}{2}$

$\huge\underline{\underline{\mathfrak{\color{teal}ThankYou}}}$