Question

3 /x-1 + 1/x+1 = 4/x​

Answer 1

$\sf\blue{Solution:-}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\sf{ \frac{3}{x - 1 }+ \frac{1}{x + 1 } = } \sf \blue{ \frac{4}{x} }$

$\sf{ \frac{3(x + 1) \: + \: 1(x - 1)}{(x - 1)(x + 1)} = } \sf \blue {\frac{4}{x} }$

$\sf{ \frac{3x \: + \: 3 \: + \: x - 1}{ {x}^{2} - 1 } =} \sf \blue{ \frac{4}{x} }$

$\sf{ \frac{4x \: + \: 2}{ {x}^{2} - 1 } = }\sf \blue{\frac{4}{x}}$

$\sf{x(4x + 2) = \: }\sf \blue{4( {x}^{2} - 1) }$

$\sf{ {4x}^{2} + 2x = \: } \sf \blue{4{x}^{2} -4 }$

$\sf{ \cancel{4x}^{2} + 2x = }\sf \blue{ \cancel4{x}^{2} -4 }$

$\sf{ 2x = \: }\sf \blue{ -4 }$

$\sf{ x = } \sf \blue{ \frac{ - \cancel4}{ \cancel2} }$

$\sf \blue{x = - 2}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\sf\blue{Steps \: follow \: to \: solve \: this \: ques :-}\downarrow$

$\sf{1) \: Same \: denominator \: of \: both \: fractions \: }$

$\sf{2) Then \: add \: them \: together}$

$\sf{3) In \: Fourth \: step \: do \: cross \: multiplication}$

$\sf{ 4)Then \: just \: simply \: solve \: both \: equation}$

$\sf{5) By \: shifting \: them \: to \: other \: side \: if \: needed}$

$\sf \blue{6) Then \: the \: value \: of \: x \: comes \: which \: is \: -2}$