SOLUTION: 1. -2/y^2 - 9 + 4y/(y - 3)^2 + 6/3 - y 2. x^2/3x^2 - 5x - 2 - 2x/3x + 1 divived by 1/x - 2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 1. -2/y^2 - 9 + 4y/(y - 3)^2 + 6/3 - y 2. x^2/3x^2 - 5x - 2 - 2x/3x + 1 divived by 1/x - 2      Log On


   

Question 268999: 1. -2/y^2 - 9 + 4y/(y - 3)^2 + 6/3 - y
2. x^2/3x^2 - 5x - 2 - 2x/3x + 1 divived by 1/x - 2
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
1. -2/(y^2 - 9) + 4y/(y - 3)^2 + 6/(3 - y)
factor the denominators to get
-2%2F%28%28y-3%29%28y%2B3%29%29+%2B+4y%2F%28y+-+3%29%5E2+%2B+6%2F%283+-+y%29
change the last sign to minus by the negative 1 rule and we get
-2%2F%28%28y-3%29%28y%2B3%29%29+%2B+4y%2F%28y+-+3%29%5E2+-+6%2F%28y-3%29
our common denominator is (y-3)^2(y+3). We change our numerators as
%28-2%2A%28y-3%29+%2B4y%28y%2B3%29+-6%28y%5E2-9%29%29%2F%28%28y-3%29%5E2%28y%2B3%29%29
simplify the numerator as
%28-2y%5E2%2B10y%2B60%29%2F%28%28y-3%29%5E2%28y%2B3%29%29
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2. %28x%5E2%2F%283x%5E2+-+5x+-+2%29+-+2x%2F%283x+%2B+1%29%29+%2F+%281%2F%28x+-+2%29%29
factor the first fractions as
%28x%5E2%2F%283x%2B1%29%28x-2%29+-+2x%2F%283x+%2B+1%29%29+%2F+%281%2F%28x+-+2%29%29
add the numerator fractions to get
%28%28x%5E2-2x%5E2%2B4x%29%2F%28%283x%2B1%29%28x-2%29%29%29+%2F+%281%2F%28x+-+2%29%29
simplifying we get
%28%28-x%5E2+%2B+4x%29%2F%28%283x%2B1%29%28x-2%29%29%29+%2F+%281%2F%28x+-+2%29%29
multiply both fractions by x-2 we get
%28-x%5E2+%2B+4x%29%2F%283x%2B1%29
if you want to factor the numerator, we get
-x%2A%28x-4%29%2F%283x%2B1%29