Can you please verify my simplified expressions and point out where I went out wrong if I made mistakes:
(3x+1)/(2x^2-2) + (2x+2)/(2x^2-8x+6)=5x+1/2(x+1)(x-3)
Oh my !!!
How about factoring first and see where that gets you?
(3x+1)/[2(x+1)(x-1)]+2(x+1)/[2(x-3)(x-1)]
[(3x+1)(x-3)+(x+1)^2 ]/[(x^2-1)(x-3)]
[ 3x^2-8x-3 +x^2+2x+1 ]/[(x^2-1)(x-3)]
[4x^2-6x-2]/[(x^2-1)(x-3)]
2[2x^2-3x-1] / [(x^2-1)(x-3)]
Thanks for your help,Damon
To verify your simplifications, let's start by adding the two fractions on the left-hand side (LHS) of the equation:
(3x + 1)/(2x^2 - 2) + (2x + 2)/(2x^2 - 8x + 6)
To add the fractions, we need a common denominator, which in this case is (2x^2 - 2)(2x^2 - 8x + 6).
Now, let's rewrite each fraction with the common denominator:
[(3x + 1)(2x^2 - 8x + 6)]/[(2x^2 - 2)(2x^2 - 8x + 6)] + [(2x + 2)(2x^2 - 2)]/[(2x^2 - 2)(2x^2 - 8x + 6)]
Expanding the numerators, we get:
[6x^3 - 24x^2 + 18x + 2x^2 - 8x + 6]/[(2x^2 - 2)(2x^2 - 8x + 6)] + [4x^3 - 4]/[(2x^2 - 2)(2x^2 - 8x + 6)]
Now, we can combine like terms in the numerators:
[6x^3 - 22x^2 + 10x + 6]/[(2x^2 - 2)(2x^2 - 8x + 6)] + [4x^3 - 4]/[(2x^2 - 2)(2x^2 - 8x + 6)]
Now, let's combine the fractions by adding the numerators:
[6x^3 - 22x^2 + 10x + 6 + 4x^3 - 4]/[(2x^2 - 2)(2x^2 - 8x + 6)]
Simplifying further, we have:
[10x^3 - 22x^2 + 10x + 2]/[(2x^2 - 2)(2x^2 - 8x + 6)]
Now let's simplify the right-hand side (RHS) of the equation:
5x + 1/2(x + 1)(x - 3)
Distributing the 1/2, we get:
5x + (1/2)(x^2 - 2x - 3)
Simplifying:
5x + (1/2)x^2 - x - (3/2)
Combining like terms:
(1/2)x^2 + 4x - (3/2)
Therefore, the simplified equation is:
[10x^3 - 22x^2 + 10x + 2]/[(2x^2 - 2)(2x^2 - 8x + 6)] = (1/2)x^2 + 4x - (3/2)
Now, you can compare your simplification to the above equation and see if it matches. If there are any differences or mistakes, revise your work and check your steps accordingly.