Question

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

Answer 1

Answer:

0, -2

Step-by-step explanation:

x/2 = x²/(x-2)

x² - 2x = 2x²

x² + 2x = 0

x(x + 2) = 0

x = 0, -2

0/2 = 0²/(0-2)

0 = 0

-2/2 = (-2)²/(-2-2)

-1 = 4/-4

-1 = -1

Answer 2

Solving the rational equation x/2 = x²/(x - 2) is;

The rational equation can be written mathematically as;

x/2 = x²/(x - 2)

By cross product;

x² - 2x = 2x²

x² + 2x = 0

x (x + 2) = 0.

x = 0 or x = -2.

To check for extraneous solutions;

For x=0;

• 0/2 = 0²/-2

• 0 = 0

For x = -2;

• -2/2 = (-2)²/(-2-2)

• -1 = 4/-4

-1 = -1.

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