7/x+5/3x=2/x-5

Question

so lcm=3x(x-5)
21(x-5)+5(x-5)=5x
21x-105+5x-25=5x
26x-130=5x
-26x to both sides
-130=-21x
divide each side by -21
-130/-21
x=6.19
is this correct
thanks for checking my work.

Answer 1

from you 2nd line, I can tell that you forgot the crucial brackets, the way you typed it would have a totally different meaning.

7/x + 5/(3x) = 2/(x+5)
ok, the LCD = 3x(x+5)

then multiply each term by that

21(x-5) + 5(x-5) = 6x , you had 5x ?????
21x - 105 + 5x - 25 - 6x = 0
20x = 130
x = 6.5

other way:
add up the left side, then cross-multiply

21/(3x) + 5/(3x) = 2/(x-5)
26/(3x) = 2/(x-5)
26x - 130 = 6x
20x = 130
x = 6.5

Answer 2

thank you for your help. I see my mistake now

Answer 3

7/x+5/3x=2/x-5

LCM = 3x(x-5)

3x(x-5)(7/x) + 3x(x-5) (5/3x) = 3x(x-5)(2/x-5)

3(x-5)7 + 5(x-5) = 2(3x)

21x -105 + 5x -25 = 6x

26x -130 = 6x

26x-26x -130 = 6x -26x

-130 = -20x

-20x/-20 = -130/-20

x = 6 1/2

Answer 4

both of you have the work the same way but one has lcm as 3x(x+5) and the other has it as 3x(x-5).
I thought it was the 3x(x-5)myself .
Which is correct?

Answer 5

You should have figured out that my one line with x+5 was a typo , since I used x-5 in throughout both of my solutions.