How do you solve #7/x+3/4=5/x#?

Question

Eva Adamson · Accepted Answer

#x = - (8) / (3)#

We have: #(7) / (x) + (3) / (4) = (5) / (x)#

Let's start by combining the fractions on the equation's left side:

#=> (28 + 3 x) / (4 x) = (5) / (x)#

Next, let's multiply by two:

#=> x (28 + 3 x) = 5 (4 x)#

#=> 3 x^(2) + 28 x = 20 x#

Now, let's subtract #20 x# from both sides:

#=> 3 x^(2) + 8 x = 0#

By factoring, we can obtain:

#=> x (3 x + 8) = 0#

#=> x = 0#

or

#=> 3 x + 8 = 0#

#=> 3 x = - 8#

#=> x = - (8) / (3)#

However, using #x = 0# in the original equation would yield undefined values.

Therefore, the only real solution to the equation is #x = - (8) / (3)#.

Isaiah Anthony · Answer

undefined To solve the equation 7/x + 3/4 = 5/x, you can follow these steps:

1. Find a common denominator for the fractions on both sides of the equation. In this case, the common denominator is 4x.

2. Multiply each term by the common denominator to eliminate the fractions. This gives you: 4x * (7/x) + 4x * (3/4) = 4x * (5/x).

3. Simplify each term. The x in the numerator and denominator of the first term cancels out, leaving you with 28 + 3x = 20.

4. Rearrange the equation by moving the constant term to the other side: 3x = 20 - 28.

5. Simplify the right side of the equation: 3x = -8.

6. Divide both sides of the equation by 3 to solve for x: x = -8/3.

Therefore, the solution to the equation 7/x + 3/4 = 5/x is x = -8/3.