Question

Solve the following equation. Remember to check for extraneous solutions 4/3x + 5/4 = 3/x.

Answer 1

The solution of the equation is x = 4/3

Explanation:

Hi there!

We have the following equation:

4/3x + 5/4 = 3/x

Subtract 3/x and 5/4 to both sides of the equation

4/3x - 3/x = -5/4

multiply both sides by x

x(4/3x - 3/x) = (-5/4)x

Apply distributive property

4/3 - 3 = (-5/4)x

-5/3 = (-5/4)x

divide both sides by (-5/4)

-5/3 / (-5/4) = x

4/3 = x

Now let´s check the solution:

4/(3 · 4/3) + 5/4 = 3/(4/3)

1 + 5/4 = 9/4

9/4 = 9/4

Then, the solution of the equation is x = 4/3

Have a nice day!