Solve the rational equation x divided by 4 equals x squared divided by quantity x plus 2 end quantity, and check for extraneous solutions.

x = 0, x = 2/3

Step-by-step explanation:

x / 4 = x² / (x + 2)

x = 4x² / (x + 2)

x * (x + 2) = 4x²

x² + 2x = 4x²

3x² - 2x = 0

x (3x - 2) = 0

x = 0, x = 2/3

x=0, 2/3

Step-by-step explanation:

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

Using cross products

4x^2 = x (x+2)

Distribute

4x^2 = x^2 + 2x

Subtract x^2 from each side

3x^2 = 2x

Subtract 2x from each side

3x^2 - 2x = 0

Factor out x

x (3x-2) = 0

Using the zero product property

x=0 3x-2 = 0

x=0 3x=2

x=0 x = 2/3

Check

x=0

0/4 = 0^2 / (0+2)

0 = 0

Check

x=2/3

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

1/6 = (4/9) / (8/3)

1/6 = 4/9 * 3/8

1/6 = 4/8 * 3/9

1/6 = 1/6

Both solutions are valid