Answer:
x = 0 and x = 2/3 are solutions to the eqution
Step-by-step explanation:
Hi there!
Let´s write the equation:
x/4 = x² / (x + 2)
Multiply both sides of the equation by (x + 2):
1/4 · x · (x + 2) = x²
Apply distributive property:
1/4 · x² + 1/2 · x = x²
Substract x² to both sides of the equation:
-x² + 1/4 · x² + 1/2 · x = 0
-3/4 · x² + 1/2 · x = 0
x(-3/4 · x + 1/2)
x = 0
and
-3/4 · x + 1/2 = 0
Substract 1/2 to both sides of the equation:
-3/4 · x = -1/2
divide by -3/4 both side of the equation:
x = -1/2 / -3/4
x = 2/3
Let´s check the solutions:
x = 0
0/4 = 0 / 0 + 2
0 = 0
x = 2/3
2/3 / 4 = (2/3)² / (2/3 + 2)
1/6 = 1/6
Then x = 0 and x = 2/3 are solutions to the eqution
