The value of x in the equation [tex]\frac{x}{2} = \frac{x^2}{x - 2}[/tex] are x = 0 and x = -2
How to solve the rational expression?
The expression is given as:
[tex]\frac{x}{2} = \frac{x^2}{x - 2}[/tex]
Cross multiply
[tex]x(x - 2) =2 * x^2[/tex]
Open the bracket
[tex]x^2 - 2x =2x^2[/tex]
Collect like terms
[tex]- 2x =2x^2 - x^2[/tex]
Evaluate the like terms
[tex]- 2x =x^2[/tex]
Rewrite as:
[tex]x^2 + 2x =0[/tex]
Factor out x
x(x + 2) =0
Expand
x = 0 or x + 2 = 0
Solve for x
x = 0 or x = -2
Hence, the value of x are x = 0 and x = -2
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