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

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.

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

thank you for your help. I see my mistake now

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

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?

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.

To solve the equation 7/x + 5/3x = 2/x - 5, let's go through the steps taken:

1. First, find the least common multiple (LCM) of the denominators. Since we have x and 3x as denominators, the LCM is 3x(x-5).

2. Multiply each term in the equation by the LCM to eliminate the fractions:

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

Simplifying the equation:

21(x-5) + 5(x-5) = 2(x-5) - 15x(x-5)

3. Expand and simplify:

21x - 105 + 5x - 25 = 2x - 10 - 15x^2 + 75x

Combining like terms:

26x - 130 = -15x^2 + 96x - 10

4. Rearrange the equation to set it equal to zero:

-15x^2 + 96x - 10 - 26x + 130 = 0

Simplifying:

-15x^2 + 70x + 120 = 0

5. Now, we can solve for x using any method you prefer, such as factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula.

The quadratic formula states that for any equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

So, for our equation -15x^2 + 70x + 120 = 0, a = -15, b = 70, and c = 120.

Plugging these values into the quadratic formula:

x = (-(70) ± sqrt((70)^2 - 4(-15)(120))) / (2*(-15))

Simplifying further:

x = (-70 ± sqrt(4900 + 7200)) / (-30)

x = (-70 ± sqrt(12100)) / (-30)

x = (-70 ± 110) / (-30)

6. Using the plus/minus symbol ±, we have two possible solutions:

x = (-70 + 110) / (-30) = 40 / -30 = -4/3

x = (-70 - 110) / (-30) = -180 / -30 = 6

Therefore, the solutions to the equation are x = -4/3 and x = 6.

Based on your calculations, it seems you made a mistake during simplification.

When you expanded the equation, the term -15x(x-5) should be -15x^2 + 75x, not -15x^2 + 96x.

So, correcting that mistake, the equation becomes:

26x - 130 = -15x^2 + 75x - 10

Remember to check your calculations and make sure you perform each step carefully.