[MOVED] solving rational equations

[Alyssa]

I'm retaking trig/pre-calculus this year, and am having trouble with some of the review material. The following is the problem I can't figure out:

I got this far, but I'm not sure I did it right...I tried to use the quadratic equation as well factoring it, and neither of them worked for me, so...yeah. Help, it's due tomorrow!

Also the back of the book says the answers are -7/5 and 2

 

[stapel]

How did you get that 5(x - 1)(x + 2) equalled (5x - 5)(5x + 10)? You would need two factors of 5 to get the second expression.

Try to show every step:

. . . . .\(\displaystyle \L \frac{1}{x\, -\, 1}\, +\, \frac{1}{x\, +\, 2}\, =\, \frac{5}{4}\)

. . . . .\(\displaystyle \L \left(\frac{4(x\, -\, 1)(x\, +\, 2)}{1}\right) \left( \frac{1}{x\, -\, 1}\right)\, +\,\left(\frac{4(x\, -\, 1)(x\, +\, 2)}{1}\right)\left( \frac{1}{x\, +\, 2}\right)\, =\,\left(\frac{4(x\, -\, 1)(x\, +\, 2)}{1}\right) \left(\frac{5}{4}\right)\)

. . . . .\(\displaystyle \L [4(x\, +\, 2)]\, +\, [4(x\, -\, 1)]\, =\, 5(x \, +\, 2)(x\, -\, 1)\)

. . . . .\(\displaystyle \L 4x\, +\, 8\, +\, 4x\, -\, 4\, =\, 5(x^2\, +\, x\, -\, 2)\)

And so forth.

Eliz.

 

[Alyssa]

Alright, so I still can't figure it out... :/

After that, I tried the quadratic equation and then I tried completing the square...And they both didn't work. Is there some trick to this problem?

 

[Denis]

Your 16x + 4 should be 8x + 4 ; gonna kick yourself :?:

Get ready for a "nice" solution...