SOLUTION: Can you help me with this problem? (2x+1)/(x+3)+(3x)/(x-2)+2x It just says perform the indicated operation. Can you help?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can you help me with this problem? (2x+1)/(x+3)+(3x)/(x-2)+2x It just says perform the indicated operation. Can you help?       Log On


   

Question 528248: Can you help me with this problem?

(2x+1)/(x+3)+(3x)/(x-2)+2x It just says perform the indicated operation. Can you help?
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
%282x%2B1%29%2F%28x%2B3%29 + %283x%29%2F%28x-2%29 + 2x

Write the term 2x as 2x%2F1, so all terms will be fractions:

%282x%2B1%29%2F%28x%2B3%29 + %283x%29%2F%28x-2%29 + 2x%2F1

The LCD is {x+3)(x-2).  We must get all three fractions to have
the LCD for the denominator by multiplying by unit fractions.

The denominator of the first fraction needs to be multiplied by 
(x-2) to become the LCD, so we multiply the first fraction by 
the unit fraction red%28%28x-2%29%2F%28x-2%29%29

The denominator of the second fraction needs to be multiplied by 
(x+3) to become the LCD, so we multiply the second fraction by 
the unit fraction red%28%28x%2B3%29%2F%28x%2B3%29%29

The denominator of the third fraction needs to be multiplied by 
(x+3)(x-2) to become the LCD, so we multiply the first fraction by 
the unit fraction red%28%28%28x%2B3%29%28x-2%29%29%2F%28%28x%2B3%29%28x-2%29%29%29


red%28%28x-2%29%2F%28x-2%29%29·%282x%2B1%29%2F%28x%2B3%29 + red%28%28x%2B3%29%2F%28x%2B3%29%29·%283x%29%2F%28x-2%29 + red%28%28%28x%2B3%29%28x-2%29%29%2F%28%28x%2B3%29%28x-2%29%29%29·2x%2F1


%28%28x-2%29%282x%2B1%29%29%2F%28%28x-2%29%28x%2B3%29%29 + %28%28x%2B3%29%283x%29%29%2F%28%28x%2B3%29%28x-2%29%29 + %28%28x%2B3%29%28x-2%29%282x%29%29%2F%28%28x%2B3%29%28x%2B2%29%29

Multiply the tops out but not the bottoms:

%282x%5E2-3x-2%29%2F%28%28x-2%29%28x%2B3%29%29 + %283x%5E2%2B9x%29%2F%28%28x%2B3%29%28x-2%29%29 + %28%28x%5E2%2Bx-6%29%282x%29%29%2F%28%28x%2B3%29%28x%2B2%29%29

%282x%5E2-3x-2%29%2F%28%28x-2%29%28x%2B3%29%29 + %283x%5E2%2B9x%29%2F%28%28x%2B3%29%28x-2%29%29 + %282x%5E3%2B2x%5E2-12x%29%2F%28%28x%2B3%29%28x%2B2%29%29

Since all the deminators are equal to the LCD, we write the sum of the
numerators over the LCD:



Remove the parentheses on top:

%282x%5E2-3x-2%2B3x%5E2%2B9x%2B2x%5E3%2B2x%5E2-12x%29%2F%28%28x%2B2%29%28x%2B3%29%29

Collect like terms in the top and arrange in descending order:

%282x%5E3%2B7x%5E2-6x-2%29%2F%28%28x%2B2%29%28x%2B3%29%29

Edwin