SOLUTION: Hi. Thank you so much for the help you have given me thus far,but I need help with this problem. I am solving rational expressions and I am having a hard time trying to solve this

Question 972651: Hi. Thank you so much for the help you have given me thus far,but I need help with this problem. I am solving rational expressions and I am having a hard time trying to solve this equation:
6+4/(x-3)=3x+1/(x-3)
I started to work this problem by multiplying each term by the LCD which is (x-3)
6(x-3)+4/x-3(x-3) + 3x+1/x-3(x-3)
Then I cross cancelled the x-3 terms which allowed me to have the equation:
6x-18 + 4=3x+1 Is this right so far? I'm not so sure that is why I hope you can help me.
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
You started well but forced a step which changes part of the equation's meaning.

Go ahead and solve for x. Use the fraction skills that you know. When you get your answer or answerS, check each of them to see if it works in the original equation. Notice that a value that you must not accept as any solution is x=3.

I see a mistake in your step.

Clear the denominators by MULTIPLYING both members by the LCD, (x-3). This gives,

and continue from this...
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