Help with some algebra 2?

Question

I need help with these questions: Solve: 4 divided by the quantity x squared minus 8 x plus 12 equals x divided by the quantity x minus 2 plus 1 divided by the quantity x minus 6 Solve: 5 divided by the quantity 5 minus p, minus p squared divided by the quantity 5 minus p equals negative 2

Answer 1

1.     I need help with these questions: Solve: 4 divided by the quantity x squared minus 8 x plus 12 equals x divided by the quantity x minus 2 plus 1 divided by the quantity x minus

   4 / (x^2 -8x + 12) = x / (x -2) +1 /(x - 6)

(x - 6) , (x -2) lcm is    (x^2 -8x + 12)

4 / (x^ 2-8x + 12) = (x *(x - 6) +1(x -2))/( x^2 -8x + 12)

4 / (x^2 -8x + 12) =(x^2 - 6x  + x - 2)/( x^2 -8x + 12)

4 / (x^2 -8x + 12) =(x^2 - 5x - 2)/( x^2 -8x + 12)

cancel common terms

  4 =x^2 - 5x - 2

subtract 4 from each side

4 - 4 =x^2 - 5x - 2 - 4

x^2 - 5x - 6 =0

x^2 - 6x +x- 6 =0

x (x - 6) +1 ( x - 6)=0

take out  common factor

(x - 6) ( x +1) =0

x -6 =0 ,  x +1 =0

x = 6   , x= -1

the solution  ( 6 , -1)

Answer 2

1.     I need help with these questions: Solve: 4 divided by the quantity x squared minus 8 x plus 12 equals x divided by the quantity x minus 2 plus 1 divided by the quantity x minus

   4 / (x^2 -8x + 12) = x / (x -2) +1 /(x - 6)

(x - 6) , (x -2) lcm is    (x^2 -8x + 12)

4 / (x^ 2-8x + 12) = (x *(x - 6) +1(x -2))/( x^2 -8x + 12)

4 / (x^2 -8x + 12) =(x^2 - 6x  + x - 2)/( x^2 -8x + 12)

4 / (x^2 -8x + 12) =(x^2 - 5x - 2)/( x^2 -8x + 12)

cancel common terms

  4 =x^2 - 5x - 2

subtract 4 from each side

4 - 4 =x^2 - 5x - 2 - 4

x^2 - 5x - 6 =0

x^2 - 6x +x- 6 =0

x (x - 6) +1 ( x - 6)=0

take out  common factor

(x - 6) ( x +1) =0

x -6 =0 ,  x +1 =0

x = 6   , x= -1

the solution  ( x =6 ,x= -1)

Answer 3

 6 Solve: 5 divided by the quantity 5 minus p, minus p squared divided by the quantity 5 minus p equals negative2

  Given  5 divided by the quantity 5 minus p, minus p squared divided by the quantity 5 minus p equals negative 2

  5 / 5-p  - p^2 / 5-p = -2

  LCM is 5-p

  5-p^2 / 5-p = -2

  Multiply each side by 5-p

  (  5-p^2 / 5-p ) * 5-p = -2* 5-p

   5 - p^2 = -2 * 5-p

  5 - p^2 = -2*5 + (-p) (-2 )

  Product of two same signs is positive

  5 - p^2 = -10 + 2p

  Subtract 5 from  each side

  5 - p^2 -5 = -10 +2p -5

  - p^2 = 2p - 15

  Add p^2 to  each side

    -  p^2 + p^2 = 2p -15 +p^2

   0 = p^2+2p -15

  p^2+2p -15 = 0

  p^2+5p -3p -15 = 0

  p(p+5 ) - 3 (p+5 ) = 0

  (  p - 3 ) ( p+5) = 0

  p-3 = 0 or p+5 = 0

  p=3 or p = -5