Question

solve as on given picture 3/x-1-2/x-2=1/x-3​

Answer 1

Answer:

$\bullet \: \: \boldsymbol x = \tt \dfrac{11}{4}$

Explanation:

Given equation,

$\boldsymbol{ \implies \: \dfrac{3}{x - 1} - \dfrac{2}{x - 2} = \dfrac{1}{x - 3} }$

Solving for $\boldsymbol x$

$\boldsymbol{ \implies \: \dfrac{3(x - 2) - 2(x - 1)}{(x - 1)(x - 2)} = \dfrac{1}{x - 3} }$

$\boldsymbol{ \implies \: \dfrac{3x - 6- 2x - 2}{ {x}^{2} - 3x + 2 } = \dfrac{1}{x - 3} }$

$\boldsymbol{ \implies \: \dfrac{x - 8}{ {x}^{2} - 3x + 2 } = \dfrac{1}{x - 3} }$

$\boldsymbol{ \implies \: {(x - 8)(x - 3)}{ } = 1({x}^{2} - 3x + 2)}$

$\boldsymbol{ \implies \: {x}^{2} - 11x + 24= {x}^{2} - 3x + 2}$

Subtracting both sides by $\boldsymbol {x^2}$

$\boldsymbol{ \implies \: - 11x + 24= - 3x + 2}$

$\boldsymbol{ \implies \: 24 - 2= 11x- 3x }$

$\boldsymbol{ \implies \: 22= 8x }$

$\boldsymbol{ \implies \: \dfrac{22}{8} = x }$

$\boldsymbol{ \implies \: \dfrac{11}{4} = x }$

${ \underline {\sf \therefore \: The \:value \: of \boldsymbol{x} \: is \: \dfrac{11}{4} }}$

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Answer 2

$\huge⚘ \bf \ \red{Answer}$

We need to find the value of x

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

On taking LCM in LHS we get

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

=>3x-9 + x-1 / (x-1)(x-3) = 4/ x-2

=> (4x -10) (x-2) = 4 (x-1) (x-3)

= >4×2 – 8x -10x+20= 4 (x2 -3x -x+3)

=> 4x2 -18x +20 = 4x2 – 12x -4x +12

=> 4x2 -18x +20 = 4x2 – 16x +12

4x2 gets cancelled on both sides

=> -18x +20 = – 16x +12

=> -18x+16x = 12 – 20

=> -2x = -8

Negative sign gets cancelled on both sides

=> 2x= 8

=> x= 8/2

=>x=4

Hence x=4