Help me solve (1-2x)/(2x+1) + (x^2+3x)/(4x^2-1) [div] (3+x)/(4x+2)

Please help me solve this equation for x:

. . . . .\(\displaystyle \dfrac{1\, -\, 2x}{2x\, +\, 1}\, +\, \dfrac{x^2\, +\, 3x}{4x^2\, -\, 1}\, \div\, \dfrac{3\, +\, x}{4x\, +\, 2}\)

Thanks so much.

leap2004 said:

Please help me solve this equation for x:

. . . . .\(\displaystyle \dfrac{1\, -\, 2x}{2x\, +\, 1}\, +\, \dfrac{x^2\, +\, 3x}{4x^2\, -\, 1}\, \div\, \dfrac{3\, +\, x}{4x\, +\, 2}\)

Thanks so much.

Click to expand...

1) Not an equation. Click that link you accidentally created (inside your post) and read more on that.

2) The general idea on such a ponderous expression is to factor every piece of it, try to rewrite it in a useful fashion, and see what factors you can eliminate.

Let's see where you go with it.

leap2004 said:

Please help me solve this equation for x:

. . . . .\(\displaystyle \dfrac{1\, -\, 2x}{2x\, +\, 1}\, +\, \dfrac{x^2\, +\, 3x}{4x^2\, -\, 1}\, \div\, \dfrac{3\, +\, x}{4x\, +\, 2}\)

Click to expand...

We'll be glad to help you "simplify" this "expression"! But we'll first need to see where you're having trouble. So please reply with a clear listing of your thoughts and efforts so far, starting with the flipping of the one fraction to convert the division to multiplication, and then showing your factorisations. Thank you!