How do you solve this problem? 3/(x-2) + 2 = 18/(x+1)?

Question

3/(x-2) + 2 = 18/(x+1)
Find the sum of all the distinct values of x.

The answer is 8.5 (I have an answer sheet) but how do you get it? Can you cross multiply even though there's a + 2?

Answer 1

I'm only in Algebra 1 so I had my dad solve it. :) I couldn't make any sense of it while my dad was explaining so I took the page he did his work on and scanned it. Here's a link to the pic: http://www.deviantart.com/deviation/49485366/
Hope you can make sense of it. If you cooridinate the image with info other people gave you, I'm sure you'll understand it. :)

btw - I cleaned it up, so if there's any problem with it, I'll just give you the original image.

Answer 2

All right. I absolutely hate factoring with fractions, and I don't really know what "the sum of all distinct values of x". But when I did the question on my own, it did equal 8.5 This is my theory:

First, you have to get rid of what's on the bottom. To do this, multiply the top by the common denominator.
3(x+1)(x-2)/(x-2) + 2(x-2)(x+1) = 18(x-2)(x+1)/(x+1)

This then becomes 3(x+1)+2(x-2)(x+1)=18(x-2), because the bottom denominator cancels out the one that is the same on top.

All right, this is the easy part. Just distribute everything so there are no brackets.
3x+3+(2x-4)(x+1)=18x-36
Continue: 3x+3+2x^2+2x-4x-4=18x-36

Now combine like terms.
2x^2-17+35=0

Now, factor this trinomial.
2x^2-10x-7x+35
2x(x-5)-7(x-5)
(2x-7)(x-5)

Now, equal both to zero to find x.
2x-7=0
2x=7
x=7/2

x-5=0
x=5

Now, add 7/2+5, because the question asks for the sum of the vales of x. It should equal 8.5

Haha, I hope you understand that. I might've made an error throughout the process at the top with the numbers, so sorry about that.

Answer 3

a million/ Get the x to a minimum of one section -4x +31 = -3x -18 upload 3x to the two factors -4x + 3x + 31 = - 3x + 3x -18 -x + 31 = -18 Now subtract 31 from the two factors -x + 31 -31 = -18 - 31 -x = -40 9 or x=40 9 2^2 + 5 - 13x + 11x - 2^2 +22 ( i think of of) only upload or subtract like words 2^2 -2^2 -13x + 11x + 5 + 22 = -2x + 27 i flow to pass away some thing so which you will have the means to coach on if that is a similar means you only upload or subtract the backside after grouping each and each and each and all of the like numbers on a similar time

Answer 4

use distributative property I believe. Multple 3 and x and 3x2 and then work it out from there on.

Answer 5

very very carfully