# How do you solve (x-2)/6=(x-2)/(x-1)?

Oct 30, 2017

ans : x = 2 and x=7

#### Explanation:

you perform cross multiplication

that is,

$$          (x-2) (x-1) = 6 (x-2)


simplifying to obtain :
${x}^{2} - x - 2 x + 2$ = $6 x - 12$

further simplify

${x}^{2} - 3 x + 2$ = 6x - 12

sending everything on the left hand side;

${x}^{2} - 3 x + 2 - 6 x + 12 = 0$

${x}^{2} - 9 x + 14 = 0$

simplify into brackets

( x- 2) ( x - 7)

therefore ans are :

x= 2 and x= 7

:)