SOLUTION: {(x+1)(2x-1)/(2x-3)(x-3)}-{(x-3)(x+1)/(3-x)(3-2x)}+ {(2x+1)(x+3)/(3-2x)(x-3) The answer I got was... 3x^2+10x+5/2x^2-9x+9 is this correct? THANK Y

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: {(x+1)(2x-1)/(2x-3)(x-3)}-{(x-3)(x+1)/(3-x)(3-2x)}+ {(2x+1)(x+3)/(3-2x)(x-3) The answer I got was... 3x^2+10x+5/2x^2-9x+9 is this correct? THANK Y      Log On


   

Question 96882This question is from textbook Introductory and Intermediate Algebra
: {(x+1)(2x-1)/(2x-3)(x-3)}-{(x-3)(x+1)/(3-x)(3-2x)}+ {(2x+1)(x+3)/(3-2x)(x-3)

The answer I got was... 3x^2+10x+5/2x^2-9x+9
is this correct?
THANK YOU so much for your help!!
 This question is from textbook Introductory and Intermediate Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given expression





Rewrite 3-x as -%28x-3%29 and %283-2x%29 as -%282x-3%29 (note: the 2nd fraction will have two negatives multiplying to a positive )



Since we are dealing with fractions, we need to find the LCD so we can combine them.

Now multiply the first two fractions by -1%2F-1. This will make every fraction have the same denominator.



Now combine the fractions.


Foil the parenthesis in the numerator


%28-2x%5E2-x%2B1%2Bx%5E2-2x-3%2B2x%5E2%2B7x%2B3%29%2F%28-1%282x-3%29%28x-3%29%29 Distribute the negative


%28-2x%5E2-x%2B1-x%5E2%2B2x%2B3%2B2x%5E2%2B7x%2B3%29%2F%28-1%282x%5E2-9x%2B9%29%29 Foil the terms in the denominator



%28-2x%5E2-x%2B1-x%5E2%2B2x%2B3%2B2x%5E2%2B7x%2B3%29%2F%28-2x%5E2%2B9x-9%29 Distribute



%28x%5E2%2B4x%2B1%29%2F%28-2x%5E2%2B9x-9%29 Combine like terms in the numerator



So simplifies to %28x%5E2%2B4x%2B1%29%2F%28-2x%5E2%2B9x-9%29


Check:

If you graph the original expression and the reduced expression on the same plot, they will line up perfectly. Since they line up, they are equivalent and this verifies our answer.