Question

x/x-1+x-1/x=2 1/2
please solve step by step
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Answer 1

Step-by-step explanation:

x−x−

2

1

=1−x−

3

2

⟹−

2

1

=1−x−

3

2

⟹−

2

1

−1+

3

2

=−x

⟹−x=

6

−3−6+4

⟹−x=

6

−9+4

⟹−x=−

6

5

⟹

x=

6

5

Answer 2

$\huge{\underline{\bf\red{Questi {\mathbb{O}} n} :}}$

Solv the below equation for x :----

$\boxed{ \frac{x}{x - 1} + \frac{x - 1}{x} = 2 \frac{1}{2} }$

$\huge{\underline{\: \bf\green{Answ {\mathbb{E}} r}\ \: :}}$

$\blue{\underline{\bf\green{\quad x = 2 \ \red{or} \ x = -1 \quad}}}$

$\huge{\underline{\bf\blue{Soluti {\mathbb{O}} n}\ :}}$

we have ,

$\begin{aligned} \red{ \frac{x}{x - 1} + \frac{x - 1}{x} }& = \red{ 2 \frac{1}{2} } \\ \\ \implies \qquad \quad \ \ \ \frac{ {(x)}^{2} + {(x - 1)}^{2} }{x(x - 1)} & = \frac{5}{2} \\ \\ \implies \qquad \quad\frac{ {x}^{2} + {x}^{2} + 1 - 2x }{ {x}^{2} - x } & = \frac{5}{2} \\ \\ \implies \qquad \quad \ \ 2 \big(2 {x}^{2} - 2x + 1 \big) & = 5 \big( {x}^{2} - x\big) \\ \\ \implies \qquad \qquad \quad4 {x}^{2} - 4x + 2 & = 5 {x}^{2} - 5x \\ \\ \implies5 {x}^{2} - 4 {x}^{2} - 5x + 4x - 2 & = 0 \\ \\ \implies \qquad \qquad \qquad {x}^{2} - x - 2 & = 0 \\ \\ \implies \qquad \quad \ \ \ {x}^{2} - 2x + x - 2 & = 0 \\ \\ \implies \qquad x(x - 2) + 1(x - 2) & = 0 \\ \\ \implies \qquad \qquad \: \ (x - 2)(x + 1) & = 0 \\ \\ \implies \boxed{ \quad \green{ x = 2 } \quad \boxed{or} \quad \green{ x = - 1} } \end{aligned}$

$\red{\rule{5.5cm}{0.02cm}}$

$\Large{ \mid {\underline{\underline{\bf\green{BrainLiest \ AnswEr}}}} \mid }$