SOLUTION: 3x+1/ 2x-6 - x+2 / x-3

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Question 118989: 3x+1/ 2x-6 - x+2 / x-3
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
You don't say what you want to do with this expression. Please be more specific in the future about what you are asked to do in the problem.

%28%283x%2B1%29%2F%28+2x-6%29%29++-+%28%28+x%2B2%29+%2F%28+x-3%29%29

Presuming that you only have to add the fractions and simplify:

Step 1: Find the LCD.

2x-6=2%28x-3%29 so 2x-6 and x-3 have a common factor of x-3. Therefore your LCD is 2x-6

Step 2: Apply the LCD.

%28%283x%2B1%29%2F%28+2x-6%29%29++-+%282%28+x%2B2%29+%2F%28+2x-6%29%29

Step 3: Apply the distributive property to the 2nd fraction's numerator

%28%283x%2B1%29%2F%28+2x-6%29%29++%2B%28-2x-4%29+%2F%28+2x-6%29%29

Step 4: Add the numerators

%28%283x%2B1%29%2B%28-2x-4%29%29%2F%28+2x-6%29

Step 5: Collect like terms

%28x-3%29%2F%282x-6%29

Step 6: Factor the denominator

%28x-3%29%2F2%28x-3%29

Step 7: Divide x-3 by x-3

cross%28x-3%29%2F%282%2Across%28x-3%29%29=1%2F2