please help me solve x

Question

anonymous · Answer

$$4+\frac{ 3 }{ x-3 }=-\frac{ 1 }{ x-2 }$$

anonymous · Answer

4(x-2)(x-3)+3(x-2)=-1(x-3)
4x^2-20x+24+3x-6=-x+3
4x^2-16x+21=0

anonymous · Answer

you should be able to get it from there

anonymous · Answer

do i just factor $$4x ^{2}-16x+21$$

anonymous · Answer

yes

anonymous · Answer

oh i see. thank you!

anonymous · Answer

i'm still very confused on this

anonymous · Answer

can someone go step by step for me please?

anonymous · Answer

Ill tell you how I started. First you have to get rid of the denominators. So multiply both sides by (x-3) then multiply both sides by (x-2)

anonymous · Answer

ok.

anonymous · Answer

Then you write out the whole equation (that just means solve until the parenthesis are gone)
you're left with this  4x^2-20x+24+3x-6=-x+3

anonymous · Answer

next you simplify.

4x^2 -17x+18=-x+3

then you move the stuff on the right side of the equation to the left side of the equation

4x^2-16x+15=0

anonymous · Answer

I just realized I had a typo on my original answer. sorry, I'm doing my own math at the same time. haha

anonymous · Answer

haha yeah. that's alright. I just did the work and I got the answer you just posted :)

anonymous · Answer

can I factor that?

anonymous · Answer

wait, I think I can

anonymous · Answer

Yes, they are (2x-5)(2x-3)

anonymous · Answer

so x= 5/2 and 3/2

anonymous · Answer

cool! i understood it! thank you so much!

anonymous · Answer

No problem! :)