how to solve

Question

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couldnt write it out

Answer 1

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

 

The first step is to eliminate the denominators.  To do this multiply both sides by (x-1) * (x-2)

One of these factors will cancel out in each of the fractional terms.

 

(3)(x-1)(x-2) - (1)(x-2) = (3x)(x-1)

 

Now it's a matter of combining like terms and solving for x.

 

3(x² - 3x + 2) - x + 2 = 3x² - 3x

 

3x² - 9x + 6 - x + 2 = 3x² - 3x

 

3x² - 3x² + -10x + 3x = -8

 

-7x = -8

 

x = 8/7

Answer 2

x ∉ {1, 2}

3 - 1/(x - 1) = 3x/(x - 2)              Multiply both sides by (x - 1)(x - 2)

3(x - 1)(x - 2) - (x - 2) = 3x(x - 1)

3(x² - 3x + 2) - x + 2 = 3x² - 3x 

3x² - 9x + 6 - x + 2 = 3x² - 3x

3x² - 10x + 8 = 3x² - 3x

-10x + 8 = - 3x

8 = 7x

8/7 = x

 

{8/7}

Answer 3

3-1/(x-1)=3x/(x-2)  put left side over common denominator

 

[3(x-1)-1]/(x-1)=3x/(x-2)

 

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

 

(3x-4)/(x-1)=3x(x-2) multiply both sides by (x-1)(x-2)

 

(3x-4)(x-2)=3x(x-1)  gives 3x²-10x+8=3x²-3x  or

-10x+8=-3x or 8=7x and so x=8/7