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PLS HELP BRAINLIEST WILL BE GIVEN TO FIRST ANSWER!

Solve the rational equation x over 5 equals x squared over quantity 4x plus 2 and check for extraneous solutions.

x = 0; x = −2 is an extraneous solution
x = 2; x = 0 is an extraneous solution
x = 0 and x = 2
x = 0 and x = −2

Respuesta :

mhanifa

Answer:

  • (C) x = 0 and x = 2

Step-by-step explanation:

Given equation:

  • x/5 = x²/(4x + 2)

Cross multiply and simplify:

  • x(4x + 2) = 5x²
  • 5x² = 4x² + 2x
  • x² - 2x = 0
  • x(x - 2) = 0
  • x = 0

or

  • x - 2 = 0 ⇒
  • x = 2

Correct choice is C

[tex]\\ \sf\longmapsto \dfrac{x}{5}=\dfrac{x^2}{4x+2}[/tex]

[tex]\\ \sf\longmapsto x(4x+2)=5x^2[/tex]

[tex]\\ \sf\longmapsto 4x^2+2x=5x^2[/tex]

[tex]\\ \sf\longmapsto x^2-2x=0[/tex]

[tex]\\ \sf\longmapsto x(x-2)=0[/tex]

[tex]\\ \sf\longmapsto x=0\:or\:x=2[/tex]

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