Question

$\frac{x - 2}{x -4} = \frac{x + 4}{x - 2 }$
LINEAR EQUATION

if u know how to solve it plz help..❤​

Answer 1

$\huge\rm\purple{answeR:}$

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$\bf{{\underline{To~solve}}:}$

$\tt \frac{x - 2}{x - 4} = \frac{x + 4}{x - 2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \\ \tt \implies (x - 2)(x - 2) = (x + 4)(x - 4) \: \: \: \: \: \: \: \: { \sf (cross \: multiplying)} \\ \\ \tt \implies {(x)}^{2} - 2(x)(2) + {(2)}^{2} = {(x)}^{2} - {(4)}^{2} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \\ \tt \implies \cancel{ \: {x}^{2} } - 4x + 4 = \cancel{ \: {x}^{2}} - 16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \\ \tt \implies - 4x + 4 = - 16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \\ \tt \implies - 4x = - 16 - 4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\ \\ \tt \implies \cancel{- }4x = \cancel - 20~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \\ \tt \implies 4x = 20~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \\ \tt \implies x = \frac{20}{4} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \\ \tt \implies x = \purple{ \underline{ \boxed{ \bf 5}}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

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$\bf\therefore{{\underline{Required~answer}}:}$

• $\large\tt{x={\purple{\underline{\underline{\bf ~5~}}}}}$

Answer 2

Answer:

x = 5

Step-by-step explanation:

\bf{{\underline{To~solve}}:}To solve:

\begin{gathered} \tt \frac{x - 2}{x - 4} = \frac{x + 4}{x - 2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \\ \tt \implies (x - 2)(x - 2) = (x + 4)(x - 4) \: \: \: \: \: \: \: \: { \sf (cross \: multiplying)} \\ \\ \tt \implies {(x)}^{2} - 2(x)(2) + {(2)}^{2} = {(x)}^{2} - {(4)}^{2} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \\ \tt \implies \cancel{ \: {x}^{2} } - 4x + 4 = \cancel{ \: {x}^{2}} - 16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \\ \tt \implies - 4x + 4 = - 16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \\ \tt \implies - 4x = - 16 - 4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\\ \\ \tt \implies \cancel{- }4x = \cancel - 20~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \\ \tt \implies 4x = 20~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \\ \tt \implies x = \frac{20}{4} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \\ \\ \tt \implies x = \purple{ \underline{ \boxed{ \bf 5}}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\end{gathered}x−4x−2=x−2x+4                                                        ⟹(x−2)(x−2)=(x+4)(x−4)(crossmultiplying)⟹(x)2−2(x)(2)+(2)2=(x)2−(4)2                                ⟹x2−4x+4=x2−16                                                    ⟹−4x+4=−16                                                                 ⟹−4x=−16−4                                                                 ⟹−4x=−20                                                                        ⟹4x=20                                                                              ⟹x=420                                                                               ⟹x=5                                                                               

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\bf\therefore{{\underline{Your~answer}}:}∴Required answer:

\large\tt{x={\pink{\underline{\underline{\bf ~5~}}}}}x= 5