(Please Help) Algebra problem?

Comments

• wayne-deguman

  June 2021

  x³ - 4x = x(x² - 4) = x(x - 2)(x + 2)

  x² + 3x + 2 = (x + 1)(x + 2)

  => x(x - 2)(x + 2)/(x + 1)(x + 2)

  i.e. x(x - 2)/(x + 1)

  >
• anonymous

  June 2021

  I wish there was a "prettier" way to show this.

  Start by factoring the numerator.

  x^3-4x = x(x^2-4) = x (x-2)(x+2)

  Next, denominator.

  (x^2+3x+2) = (x+2) (x+1).

  Lastly, remove common factors:

  x ( x -2 ) / (x + 1)
• la-console

  June 2021

  = (x³ - 4x) / (x² + 3x + 2) → you factorize x

  = x(x² - 4) / (x² + 3x + 2) → you know that: 4 = 2²

  = x(x² - 2²) / (x² + 3x + 2) → you recognize: a² - b² = (a + b)(a - b)

  = x(x + 2)(x - 2) / (x² + 3x + 2) → you know that: 3x = 2x + x

  = x(x + 2)(x - 2) / [x² + (2x + x) + 2] → you group

  = x(x + 2)(x - 2) / [(x² + 2x) + (x + 2)]

  = x(x + 2)(x - 2) / [x(x + 2) + (x + 2)] → you factorize (x + 2)

  = x(x + 2)(x - 2) / [(x + 2)(x + 1)] → you simplify by (x + 2)

  = x(x - 2) / (x + 1)
• shai

  June 2021

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

  x(x^2-4) / (x+2)(x+1) =

  x(x+2)(x-2) / (x+2)(x+1) =

  cancel (x+2) :

  x(x-2) / (x+1)

  x can't be -1, -2
• como

  June 2021

  x (x² - 4)

  ----------------

  (x + 2)(x + 1)

  x (x - 2)(x + 2)

  -------------------

  (x + 2)(x + 1)

  x (x - 2)

  ------------

  x + 1
• norebal

  June 2021

  Factor the numerator and denominator:

  x ( x^2 - 4 ) ....x ( x + 2)( x - 2 )

  ----------------- = ----------------------------- .............. Cancel common factors

  x^2 + 3x + 1 .... ( x + 2 )( x + 1 )

  x ( x - 2 ) ..... x^2 - 2x

  --------------- = ---------------- THE ANSWER

  x + 1 ----------- x + 1
• anonymous

  June 2021

  x^5+3x^4-2x^3-12x^2-8x