SOLUTION: I need to simplify 2 rational expressions. Please help with showing steps so I can learn how to do for my college algebra class. Thanks!!! 3y/(y^2-7y+10)-2y/(y^2-8y+15) the 2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need to simplify 2 rational expressions. Please help with showing steps so I can learn how to do for my college algebra class. Thanks!!! 3y/(y^2-7y+10)-2y/(y^2-8y+15) the 2      Log On


   

Question 467479: I need to simplify 2 rational expressions. Please help with showing steps so I can learn how to do for my college algebra class. Thanks!!!
3y/(y^2-7y+10)-2y/(y^2-8y+15)
the 2nd one is a complex rational expression:
(1-x)/(x)+(x)/(1+x) over (fraction) (1+x)/(x)+(x)/(1-x) <----simplify
(If I need to rewrite so this one makes sense let me know)
Found 2 solutions by mananth, lwsshak3:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
3y%2F%28y%5E2-7y%2B10%29-2y%2F%28y%5E2-8y%2B15%29
3y%2F%28%28y-5%29%28y-2%29%29-2y%2F%28%28y-3%29%28y-5%29%29

LCD = (y-5)(y-2)(y-3)

%283y%28y-3%29-2y%28y-2%29%29%2F%28%28y-5%29%28y-2%29%28y-3%29%29
%283y%5E2-9y-2y%5E2%2B4y%29%2F%28%28y-5%29%28y-2%29%28y-3%29%29
%28y%5E2-5y%29%2F%28%28y-5%29%28y-2%29%28y-3%29%29
%28y%28cross%28y-5%29%29%2F%28%28cross%28y-5%29%29%28y-2%29%28y-3%29%29%29
y%2F%28%28y-2%29%28y-3%29%29


the 2nd one is a complex rational expression:
(1-x)/(x)+(x)/(1+x) over (fraction) (1+x)/(x)+(x)/(1-x) <----simplify
%28%281-x%29%2Fx%29+%2B%28x%2F%281%2Bx%29%29/%281%2Bx%29%2Fx+%2B+x%2F%281-x%29
%281-x%5E2%2Bx%5E2%29%2F%28x%281%2Bx%29%29/%28%281-x%5E2%29%2Bx%5E2%29%2F%28x%281-x%29%29
1%2F%28x%281%2Bx%29%29* %28x%281-x%29%29%2F1
%281-x%29%2F%281%2Bx%29

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
I need to simplify 2 rational expressions. Please help with showing steps so I can learn how to do for my college algebra class. Thanks!!!
3y/(y^2-7y+10)-2y/(y^2-8y+15)
the 2nd one is a complex rational expression:
(1-x)/(x)+(x)/(1+x) over (fraction) (1+x)/(x)+(x)/(1-x)
...
first problem
3y/(y^2-7y+10)-2y/(y^2-8y+15)
3y/(y-2)(y-5)-2y/(y-5)(y-3)
LCD:(y-2)(y-3)(y-5)
3y(y-3)-2y(y-2)/(y-2)(y-3)(y-5)
3y^2-3y-2y^2+4y/(y-2)(y-3)(y-5)
y^2+y/(y-2)(y-3)(y-5)
y(y+1)/(y-2)(y-3)(y-5) (This does not appear to be very simplified, but at least it is in factored form.)
..
2nd problem
[(1-x)/x+x/(1+x)]/[(1+x)/x+x/(1-x)]
working numerator and denominator separately
numerator:
(1-x)/x+x/(1+x)
LCD:x(1+x)
(1-x)(1+x)+x^2/x(1+x)
1-x^2+x^2/x(1+x)
1/x(1+x)
..
denominator:
(1+x)/x+x/(1-x)
LCD: x(1-x)
(1+x)(1-x)+x^2/x(1-x)
1-x^2+x^2/x(1-x)
1/x(1-x)
..
put numerator and denominator back together
1/x(1+x)/1/x(1-x)
1/x(1+x)/1/x(1-x)
(1-x)/(1+x) (ans)