Question

*ANSWER FAST* x-1/x-2 + x-3/x-4 = 3 1/3 [x≠2 , x≠4] find

Answer 1

Explanation:

x-1/x-2+x-3/x-4=31/3

3(x²-4x-x+4)+3(x²-2x-3x+6)=31(x²-4x-2x+8)

3(x²-5x+4)+3(x²-5x+6)=31(x²-6x+8)

3x²-15x+12+3x²-15x+18=31x²-186x+248

3x²+3x²-31x²-15x-15x+186x+12+18-248=0

-25x²+156x-218=0

-(25x²-156+218)=0

By using quadratic equation

x=

Answer 2

x = 5, x =
`(5)/(2)`

Explanation:

Given

`(x-1)/(x-2)` +
`(x-3)/(x-4)` = 3
`(1)/(3)`

`((x-1)(x-4)+(x-3)(x-2))/((x-2)(x-4))` =
`(10)/(3)`

`(x^2-5x+4+x^2-5x+6)/(x^2-6x+8)` =
`(10)/(3)`

`(2x^2-10x+10)/(x^2-6x+8)` =
`(10)/(3)` ( cross- multiply )

10(x² - 6x + 8) = 3(2x² - 10x + 10) ← distribute both sides

10x² - 60x + 80 = 6x² - 30x + 30 ← subtract 6x² - 30x + 30 from both sides

4x² - 30x + 50 = 0 ( divide through by 2 )

2x² - 15x + 25 = 0 ← in standard form

(2x - 5)(x - 5) = 0 ← in factored form

Equate each factor to zero and solve for x

2x - 5 = 0 ⇒ 2x = 5 ⇒ x =
`(5)/(2)`

x - 5 = 0 ⇒ x = 5