Question

plz help me with this question ​

Answer 1

Answer:

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

(x²-4x-x+4)+(x²-2x-3x+6)/(x²-4x-2x+8)=10/3

x²-5x+4+x²-5x+6/x²-6x+8=10/3

2(x²-5x+5)/x²-6x+8=10/3

x²-5x+5/x²-6x+8=5/3

3x²-15x+15=5x²-30x+40

2x²-15x+25=0

2x²-10x-5x+25=0

2x(x-5)-5(x-5)=0

(x-5) (2x-5)=0

x=5 or x=5/2

Answer 2

Step-by-step explanation:

$\frac{x - 1}{x - 2} + \frac{x - 3}{x - 4} = \frac{10}{3}$

On taking LCM we get

$\frac{( x - 1)(x - 4) + (x - 3)(x - 2)}{(x - 2)(x - 4)} = \frac{10}{3}$

$\frac{ {x}^{2} - 5x + 4 + {x}^{2} - 5x + 6 }{ {x}^{2} - 6x + 8} = \frac{10}{3}$

$\frac{ 2 {x}^{2} - 10x + 10 }{ {x}^{2} - 6x + 8 } = \frac{10}{3}$

on cross multiplying we get

$6 {x}^{2} - 30x + 30 = 10 {x}^{2} - 60x + 80$

On shifting all the terms to right side we get

$4 {x}^{2} - 30x + 50 = 0$

or , we can simply it and write it as

$2 {x}^{2} - 15x + 25 = 0$

$2 {x}^{2} - 10x - 5x + 25 = 0$

$2x(x - 5) - 5(x - 5) = 0$

$(2x - 5)(x - 5) = 0$

Therefore

(2x-5)=0 or (x-5)=0

x=5/2 or x=5

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