Question

Solve for x : x-1/x+2+x-3/x-4

Plz tell correct answer


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Plz help

Answer 1

Correct Question :-

• Solve for x: (x-1/x-2) + (x-3/x-4) = 10/3 ..

Solution :-

→ (x-1/x-2) + (x-3/x-4) = 10/3

Taking LCM ,

→ [(x-1)(x-4) + (x-2)(x-3)] / (x-2)(x-4)= 10/3

→ [ (x² - 5x+ 4)+ (x² - 5x +6) ] / (x^2 -6x +8) = 10/3

Cross - Multiply,

→ 3(2x² -10 x +10) = 10(x² - 6x +8)

→ 6x² -30x + 30 = 10x² - 60x + 80

→ 10x² - 6x² - 60x + 30x + 80 - 30 = 0

→ 4x² - 30x + 50 = 0

→ 2(2x² - 15x + 25) = 0

→ 2x² - 15x + 25 = 0

Splitting The Middle Term Now,

→ 2x² - 10x - 5x + 25 = 0

→ 2x(x - 5) - 5(x - 5) = 0

→ (x - 5)(2x - 5) = 0

Putting Both Equal to Zero Now,

→ x - 5 = 0

→ x = 5 (Ans).

Or,

→ 2x - 5 = 0

→ 2x = 5

→ x = (5/2) (Ans.)

Hence, Value of x is 5 or (5/2).

Answer 2

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Question-

Solve for x : x-1/x+2+x-3/x-4

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Solution-

➠x-1/x+2+x-3/x-4 = 10/3

➠[(x-1)(x-4) + (x-2)(x-3)] ÷ (x-2)(x-4) = 10/3

➠[(x² - 5x + 4) + (x² - 5x + 6)] ÷ (x² - 6x + 8) = 10/3

➠3(2x²-10x+10) = 10(x² - 6x + 8)

➠6x² - 30x + 30 = 10x² - 60x + 80

➠10x² - 6x² - 60x + 30x + 80 - 30 = 0

➠4x² - 30x + 50 = 0

➠2(2x²-15x + 25) = 0

➠2x² -15x + 25 = 0

➠2x² - 10x - 5x + 25 = 0

➠2x(x -5 ) - 5(x-5) = 0

➠(x -5)(2x - 5) = 0

➠x - 5 = 0

➠x = 5

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