Question

3/x-2 -2/x-3 = 4/x-3 -3/x-1 is getting cutted ​

Answer 1

Step-by-step explanation:

$\tt \implies\dfrac{ 3 }{ x-2 } - \dfrac{ 2 }{ x-3 } = \dfrac{ 4 }{ x-3 } - \dfrac{ 3 }{ x-1 }$

$\tt \implies\left(x-3\right)\left(x-1\right)\times 3-\left(x-2\right)\left(x-1\right)\times 2=\left(x-2\right)\left(x-1\right)\times 4-\left(x-3\right)\left(x-2\right)\times 3$

$\tt \implies\left(x^{2}-4x+3\right)\times 3-\left(x-2\right)\left(x-1\right)\times 2=\left(x-2\right)\left(x-1\right)\times 4-\left(x-3\right)\left(x-2\right)\times 3$

$\tt \implies3x^{2}-12x+9-\left(x-2\right)\left(x-1\right)\times 2=\left(x-2\right)\left(x-1\right)\times 4-\left(x-3\right)\left(x-2\right)\times 3$

$\tt \implies3x^{2}-12x+9-\left(x^{2}-3x+2\right)\times 2=\left(x-2\right)\left(x-1\right)\times 4-\left(x-3\right)\left(x-2\right)\times 3$

$\tt \implies3x^{2}-12x+9-\left(2x^{2}-6x+4\right)=\left(x-2\right)\left(x-1\right)\times 4-\left(x-3\right)\left(x-2\right)\times 3$

$\tt \implies3x^{2}-12x+9-2x^{2}+6x-4=\left(x-2\right)\left(x-1\right)\times 4-\left(x-3\right)\left(x-2\right)\times 3$

$\tt \implies \: x^{2}-12x+9+6x-4=\left(x-2\right)\left(x-1\right)\times 4-\left(x-3\right)\left(x-2\right)\times 3$

$\tt \implies \: x^{2}-6x+9-4=\left(x-2\right)\left(x-1\right)\times 4-\left(x-3\right)\left(x-2\right)\times 3$

$\tt \implies \: x^{2}-6x+5=4x^{2}-12x+8-\left(x-3\right)\left(x-2\right)\times 3$

$\tt \implies \: x^{2}-6x+5=4x^{2}-12x+8-\left(3x^{2}-15x+18\right)$

$\tt \implies \: x^{2}-6x+5=x^{2}-12x+8+15x-18$

$\tt \implies \: x^{2}-6x+5-x^{2}=3x-10$

$\tt \implies-6x+5=3x-10$

$\tt \implies-9x+5=-10$

$\tt \implies-9x=-15$

$\tt \implies \: x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$