Please simplify the difference!: ((x^2+2x+8)/(x^2-3x-10)) - ((x^2-2x-3)/(x^2+7x-6)). The material the entire course was based on was taught using a learning style I cannot work with whatsoever and because of that, I retained nothing from the course. This is more of a study question for me than anything. Please help...
3 answers
I ended up typing out the question wrong... Sorry!! It's 3 AM and I'm so tired.
If the question is wrong, how do you expect help?
Anyway, working with what you gave,
(x^2+2x+8)/(x^2-3x-10) - (x^2-2x-3)/(x^2+7x-6)
= (x^2+2x+8)/((x-5)(x+2)) - (x+1)(x-3)/(x^2+7x-6)
I'm sorry, but that does not simplify too well. Let's try
(x^2-2x-8)/(x^2-3x-10) - (x^2-2x-3)/(x^2+7x+6)
= (x-4)(x+2) / (x-5)(x+2) - (x+1)(x-3) / (x+1)(x+6)
= (x-4)/(x-5) - (x-3)/(x+6)
= ((x-4)(x+6) - (x-3)(x-5)) / ((x-5)(x-6))
= (10x-39)/(x^2-11x+30)
Anyway, working with what you gave,
(x^2+2x+8)/(x^2-3x-10) - (x^2-2x-3)/(x^2+7x-6)
= (x^2+2x+8)/((x-5)(x+2)) - (x+1)(x-3)/(x^2+7x-6)
I'm sorry, but that does not simplify too well. Let's try
(x^2-2x-8)/(x^2-3x-10) - (x^2-2x-3)/(x^2+7x+6)
= (x-4)(x+2) / (x-5)(x+2) - (x+1)(x-3) / (x+1)(x+6)
= (x-4)/(x-5) - (x-3)/(x+6)
= ((x-4)(x+6) - (x-3)(x-5)) / ((x-5)(x-6))
= (10x-39)/(x^2-11x+30)
Thank you for the help, teacher. I really appreciate it!
3 answers