Please help. I do not know how to do this. Solve: 2/3x + 4/x = 7/x+1

Assuming you mean

2/(3x) + 4/x = 7/(x+1)
then multiply through by (3x)(x+1) and you have (with x≠0 or -1)

2(x+1) + 4*3(x+1) = 7(3x)
2x+2 + 12x+12 = 21x
7x = 14
x = 2

Thank you!

To solve the equation 2/3x + 4/x = 7/x + 1, we need to simplify and manipulate the equation to isolate the variable x. Here's how to proceed step-by-step:

Step 1: Get rid of the denominators.
To do this, we can multiply each term in the equation by the least common denominator (LCD) of the fractions involved, which in this case is 3x(x + 1). Multiplying each term by 3x(x + 1) gives:

(3x)(2/3x) + (3x)(4/x) = (3x)(7/x) + (3x)(1)

This simplifies to:
2(x + 1) + 12 = 21 + 3x

Step 2: Simplify the equation.
We can start by distributing 2 to (x + 1):

2x + 2 + 12 = 21 + 3x

Combining like terms, we have:
2x + 14 = 21 + 3x

Step 3: Isolate the variable terms.
To isolate the variable terms, we need to move all the x terms to one side of the equation. Let's subtract 2x from both sides:

2x - 2x + 14 = 21 + 3x - 2x

Simplifying this gives:
14 = 21 + x

Step 4: Solve for x.
Next, we want to get rid of the constant term 21 by subtracting 21 from both sides:

14 - 21 = x

Simplifying further, we have:
-7 = x

Therefore, the solution to the equation 2/3x + 4/x = 7/x + 1 is x = -7.

To solve the equation 2/3x + 4/x = 7/x+1, we need to get rid of the fractions by finding a common denominator.

The least common denominator (LCD) for 3x, x, and x+1 is 3x(x+1). To eliminate the denominators, we will multiply every term in the equation by the LCD.

Multiplying both sides of the equation by 3x(x+1), we have:
(3x(x+1))(2/3x) + (3x(x+1))(4/x) = (3x(x+1))(7/x+1)

Simplifying, we get:
2(x+1) + 4(3(x+1)) = 7(3x)

Expanding and distributing, we have:
2x + 2 + 12x + 12 = 21x

Combining like terms, we get:
14x + 14 = 21x

Now, we can isolate the variable x by moving all the terms with x to one side and the constant terms to the other side.

Subtracting 14x from both sides, we have:
14 = 7x

Dividing both sides by 7, we get:
x = 2

Therefore, the solution to the equation 2/3x + 4/x = 7/x+1 is x = 2.