Find two rational expressions that have a sum of 9-9x/x^2-9
I need steps not just answers
3 answers
First, I assume you mean (9-9x)/(x^2-9)?
Making the same assumption as Ryan
9[(1-x)]/(x-3)(x+3)=9[a/(x-3)+b/(x+3)]
a(x+3) + b(x-3) = 1-x
a+b=-1
3a-3b=1
solve and get a =-1/3, b=-2/3
so
9 [(-1/3)/(x-3) -(2/3)/(x+3)]
= -3/(x-3) -6/(x+3)
9[(1-x)]/(x-3)(x+3)=9[a/(x-3)+b/(x+3)]
a(x+3) + b(x-3) = 1-x
a+b=-1
3a-3b=1
solve and get a =-1/3, b=-2/3
so
9 [(-1/3)/(x-3) -(2/3)/(x+3)]
= -3/(x-3) -6/(x+3)
If my assumption is true, you could simply use 9/(x^2-9) + -9x/(x^2+9), as these are both rational expressions, I think.
2 answers