Question

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x-2÷x-4=x+4÷x-2 solve for x​

Answer 1

Answer:

$\huge{\boxed{\boxed{\sf{x=5}}}}$

Step-by-step explanation:

$\huge{\boxed{\boxed{\underline{\sf{SOLUTION-}}}}}$

>>We have to find the value of x:

$\frac{x - 2}{x - 4} = \frac{x + 4}{x - 2} \\ = ) ({x - 2} )(x - 2)= (x + 4)(x - 2) \\ > > we \: use \: ({x - y})^{2} = {x}^{2} + {x}^{2} - 2xy \\ in \: lhs \: side\\ > > and {x}^{2} - {y}^{2} =( x + y)(x - y) \: \\ in \: rhs \: side \\ = ) ( {x - 2})^{2} = {x}^{2} - {4}^{2} \\ = ) {x}^{2} + {2}^{2} - 2 \times x \times 2 = {x}^{2} - 16 \\ = ){x}^{2} + 4 - 4x = {x}^{2} - 16 \\ = ) {x}^{2} - {x}^{2} + 4 + 16 - 4x = 0 \\ = )20 - 4x = 0 \\ = ) - 4x = - 20 \\ = ) x = \frac{ - 20}{ - 4} \\ = )x = 5$

$\huge{\boxed{\boxed{\sf{x=5}}}}$

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