how to find x when x/3 + (1/(x-2)) =2

Question

beth12345 · Answer

$$\frac{ x }{ 3 } + \frac{ 1 }{ x-2 } = 2$$  i find it easier to understand when its written in this form

campbell_st · Answer

multiply each term by 3(x-2) this will eliminate the fraction

which will give

$$x(x-2) + 3 = 2 \times 3(x-2)$$

next you need to expand and simplify. 

Write the equation will all terms on the left and equal to zero. 

Then you need to solve the resulting quadratic

beth12345 · Answer

how do i get both sides to be multiplied by x-2?

beth12345 · Answer

like wouldn't it cancel out?

campbell_st · Answer

(x - 2) is the denominator of the 2nd term. the common denominator is 3(x-2) 

by multiplying by the common denominator you eliminate all denominators

beth12345 · Answer

ok

beth12345 · Answer

so would it become x+1=2X3(x-2) ?

beth12345 · Answer

$$x+1=2\times 3(x-2)$$

beth12345 · Answer

oh ok nvm, i see how you did that

beth12345 · Answer

i was multiplying everything on the left as one term

beth12345 · Answer

would it afterward become (x-5)(x-3) ?

beth12345 · Answer

=0 *

beth12345 · Answer

and then x= 5 or 3 and x=/=2 ?

beth12345 · Answer

ok ya i got it, thanks