Algebraic Simplifying?

Question

Would you please explain to me how to get the answer of this problem.

( x + 2) / (2x^2 + 5x + 2) + (x - 3) / (2x^2 - 5x - 3)

Answer 1

2x^2+5x+2
=2x^2+4x+x+2
=2x(x+2)+1(x+2)
=(x+2)(2x+1)
2x^2-5x-3
=2x^2-6x+x-3
=2x(x-3)+1(x-3)
=(x-3)(2x+1)
Therefore given expression
=(x+2)/(x+2)(2x+1) +(x-3)/(x-3)(2x+1)
=1/(2x+1) +1/(2x+1)
=2/(2x+1)

Answer 2

(x+2)/(2x^2 + 4x +x + 2) + (x-3) / (2x^2-6x+x-3)

(x+2)/(2x(x+2) + 1(x+2)) + (x-3) / ( 2x(x-3) + 1(x-3))

(x+2) / (2x+1)(x+2) + (x-3) / (2x+1)(x-3)

1 / (2x + 1) + 1 / (2x+1)

2 / (2x+1)

Hope this helps. Cheers!

fatbutler.com

Answer 3

( x + 2) / (2x^2 + 5x + 2) + (x - 3) / (2x^2 - 5x - 3)
=(x+2)/[(2x+1)(x+2)] + (x-3)/[(2x+1)(x-3)]
1/(2x+1) + 1/(2x+1)
= 2/(2x+1)

Answer 4

well if those up-arrows are suppose to be exponents,and those slashes mean multiply, then i think i can help....

the answer i got is 4x^3-2x^2+13
(in other words: four x cubed - two x squared + thirteen)

and i got that but distributing (x+2); first distributing the x, then the 2. add like terms. then, distribute (x-3), just like (x-2).
collect like terms. and you should get the answer.

hope that helped

Answer 5

(x+2)/(2x+1 )(x+2) + (x-3)/ (2x-1)(x-3)
1/(2x+1 ) + 1/(2x-1)
[ (2x-1) +(2x+1 ) ] /[ (2x+1 ) (2x-1) ]
4x / [ (2x+1 ) (2x-1) ]
4x / (4x^2 -1)