LCD not working to remove fractions: (x+4)/5-(x+3)/3=-7/15

[mindfullsilence]

solving for x so far has been a breeze. Maybe it's because I've been working on catching up on my homework for the past 4 days straight with a couple hours of sleep each night, but I'm stumped

(x+4)/5-(x+3)/3=-7/15

When trying to solve, so far I've gotten up to three different answers, none of them correct. Here's the steps I've taken that haven't worked. x should equal 2 according to the answers in the back of my book.

Solving for x:
(x+4)/5-(x+3)/3=-7/15

Multiply the LCD on both sides:
15( [x+4]/5 - [x+3]/3 ) = 15(-7/15)
(15x+60)/5 -(15x+45)/3 = -105/15

simplify:
(3x+12)+(-5x+15) = -7

combine like terms: 3x + -5x, and 12+15
-2x + 27 = -7

Subtract 27 from both sides:
-2x + 27 - 27 = -7 - 27
-2x = -34

Divide each side by 2:
(-2x)/2 = (-34)/2
-x = -17

Divide each side by -1:
(-x) / -1 = (-17) / -1
x = 17

Solution:
x = 17

Obviously not right... Anyone know where I went wrong?

 

[skeeter]

Re: LCD not working to remove fractions

solving for x so far has been a breeze. Maybe it's because I've been working on catching up on my homework for the past 4 days straight with a couple hours of sleep each night, but I'm stumped

(x+4)/5-(x+3)/3=-7/15

When trying to solve, so far I've gotten up to three different answers, none of them correct. Here's the steps I've taken that haven't worked. x should equal 2 according to the answers in the back of my book.

Solving for x:
(x+4)/5-(x+3)/3=-7/15

Multiply the LCD on both sides:
15( [x+4]/5 - [x+3]/3 ) = 15(-7/15)
(15x+60)/5 -(15x+45)/3 = -105/15

simplify:
(3x+12)+(-5x-15) = -7 ... right here, see the sign error?

... Anyone know where I went wrong?