Question

Q:-5/x-2+1/x-1=6/x,where x not equal to 0,1,2​

Answer 1

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$\red{\bold{\underline{\underline{QUESTION:-}}}}$

Q:-5/x-2+1/x-1=6/x,where x not equal to 0,1,2

$\huge\orange{\overbrace{\red{\underbrace\color{blue}{\underbrace\color{black}{\colorbox{lime}{{\red\:{「Answer」}}}}}}}}$

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _✍️

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$⟹ \bold{\frac{5}{x - 2} + \frac{1}{x - 1} = \frac{6}{x}}$

$⟹\bold{ \frac{5(x - 1) + x - 2}{(x - 1)(x - 2)} = \frac{6}{x}}$

$⟹\bold{ \frac{5x - 5 + x - 2}{(x - 2)(x - 1)} = \frac{6}{x}}$

$⟹\bold{ \frac{6x - 7}{(x - 2)(x - 1)} = \frac{6}{x}{$

$⟹\bold{ \frac{x(6x - 7)}{x(x - 1) - 2(x - 1)} = \frac{6}{x} }$

$⟹\bold{ \frac{ {x}^{2} - 7x}{ {x}^{2} - x - 2x + 2} = \frac{6}{x}}$

$⟹ \bold{ {x}^{3} - 7 {x}^{2} = 6 {x}^{2} - 18x + 12}$

$⟹\bold{ {x}^{3} - 13 {x}^{2} + 18x - 12}$

$⟹\bold{ {x}^{2} (x - 13) + 6(3x - 2)}$

$⟹\bold{( {x}^{2} + 6)(x - 13)(3x - 2) = 0}$

$⟹ \bold{{x}^{2} + 6 = 0}$

$⟹\bold{\red{x =± \sqrt{6}}}$✓

$⟹\bold{x - 13 = 0}$

$⟹\bold{\red{x = 13}}$✓

$⟹\bold{3x - 2 = 0}$

$⟹\bold{\red{x = \frac{2}{3}}}$✓

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HOPE IT HELPS YOU..

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Thankyou:)

Answer 2

Step-by-step explanation:

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℘ɧεŋσɱεŋศɭ

☘

\red{\bold{\underline{\underline{QUESTION:-}}}}

QUESTION:−

Q:-5/x-2+1/x-1=6/x,where x not equal to 0,1,2

\huge\orange{\overbrace{\red{\underbrace\color{blue}{\underbrace\color{black}{\colorbox{lime}{{\red\:{「Answer」}}}}}}}}

「Answer」

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══════════XXX═════════════

⟹ \bold{\frac{5}{x - 2} + \frac{1}{x - 1} = \frac{6}{x}}⟹

x−2

5

+

x−1

1

=

x

6

⟹\bold{ \frac{5(x - 1) + x - 2}{(x - 1)(x - 2)} = \frac{6}{x}}⟹

(x−1)(x−2)

5(x−1)+x−2

=

x

6

⟹\bold{ \frac{5x - 5 + x - 2}{(x - 2)(x - 1)} = \frac{6}{x}}⟹

(x−2)(x−1)

5x−5+x−2

=

x

6

⟹\bold{ \frac{6x - 7}{(x - 2)(x - 1)} = \frac{6}{x}{

⟹\bold{ \frac{x(6x - 7)}{x(x - 1) - 2(x - 1)} = \frac{6}{x} }⟹

x(x−1)−2(x−1)

x(6x−7)

=

x

6

⟹\bold{ \frac{ {x}^{2} - 7x}{ {x}^{2} - x - 2x + 2} = \frac{6}{x}}⟹

x

2

−x−2x+2

x

2

−7x

=

x

6

⟹ \bold{ {x}^{3} - 7 {x}^{2} = 6 {x}^{2} - 18x + 12}⟹x

3

−7x

2

=6x

2

−18x+12

⟹\bold{ {x}^{3} - 13 {x}^{2} + 18x - 12}⟹x

3

−13x

2

+18x−12

⟹\bold{ {x}^{2} (x - 13) + 6(3x - 2)}⟹x

2

(x−13)+6(3x−2)

⟹\bold{( {x}^{2} + 6)(x - 13)(3x - 2) = 0}⟹(x

2

+6)(x−13)(3x−2)=0

⟹ \bold{{x}^{2} + 6 = 0}⟹x

2

+6=0

⟹\bold{\red{x =± \sqrt{6}}}⟹x=±

6

✓

⟹\bold{x - 13 = 0}⟹x−13=0

⟹\bold{\red{x = 13}}⟹x=13 ✓

⟹\bold{3x - 2 = 0}⟹3x−2=0

⟹\bold{\red{x = \frac{2}{3}}}⟹x=

3

2

✓

══════════XXX═════════════

HOPE IT HELPS YOU..

_____________________

Thankyou:)