4/x=x+3 how do you solve and check

x = 1 or x = - 4

Step-by-step explanation:

Solve for x over the real numbers:

4/x = x + 3

Multiply both sides by x:

4 = x (x + 3)

4 = x (x + 3) is equivalent to x (x + 3) = 4:

x (x + 3) = 4

Expand out terms of the left hand side:

x^2 + 3 x = 4

Add 9/4 to both sides:

x^2 + 3 x + 9/4 = 25/4

Write the left hand side as a square:

(x + 3/2) ^2 = 25/4

Take the square root of both sides:

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

Subtract 3/2 from both sides:

x = 1 or x + 3/2 = - 5/2

Subtract 3/2 from both sides:

Answer: x = 1 or x = - 4