Question

1 by x minus 1 into x minus 2 + 1 by x minus 2 into x minus 3 is equals to 2 by 3 solve for x​

Answer 1

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Answer 2

The values of x are 0 and 4.

Step-by-step explanation:

Consider the given equation is

$\dfrac{1}{\left(x-1\right)\left(x-2\right)}+\dfrac{1}{\left(x-2\right)\left(x-3\right)}=\dfrac{2}{3}$

Taking LCM on left side we get

$\dfrac{(x-3)+(x-1)}{\left(x-1\right)\left(x-2\right)(x-3)}=\dfrac{2}{3}$

$\dfrac{2x-4}{\left(x-1\right)\left(x-2\right)(x-3)}=\dfrac{2}{3}$

$\dfrac{2(x-2)}{\left(x-1\right)\left(x-2\right)(x-3)}=\dfrac{2}{3}$

Cancel out common factors.

$\dfrac{2}{\left(x-1\right)(x-3)}=\dfrac{2}{3}$

Divide both sides by 2.

$\dfrac{1}{\left(x-1\right)(x-3)}=\dfrac{1}{3}$

$3=(x-1)(x-3)$

$3=x^2-3x-x+3$

$0=x^2-4x$

$0=x(x-4)$

Using zero product property we get

$x=0,x=4$

Therefore, the values of x are 0 and 4.

#Learn more

Solve the equation for x:

1/x+1 +2/x+2 = 7/x+5, x≠-1,-2,-5.

https://brainly.in/question/12375001