Question

Adjunte una imagen con los problemas

Answer 1

SOLUCIÓN:

 4) a) x²-1 / x+1 = ( x+1)(x-1)/(x+1) = x-1

    b)  x²+1/(x-1)² = x²+1 /(x-1)(x-1)

    c) x² -4 /2x-4 =(x+2)(x-2)/2(x-2)= (x+2)/2

     d) x²+4x +4 / x²-4 = ( x+2)²/(x+2)(x-2)= (x+2)/(x-2)

     e) x²+3x/x²+x-6= x(x+3)/(x +3 )( x - 2)= x/(x-2)

    f) x²+2x-3/x²-x² = ( x +3)(x-1 )/ 0 = ∞

     g) x²+4x²+3x/x²+x-6= x( 5x +3)/(x+3)(x-2)

5) opera y simplifica:

   a) [4/x-x] 1/x +1/2 = [4-x²/x ]:1/x +1/2 = x*(4-x²)/x +1/2 = 4-x²+1/2 =

   = (8-2x²+1 )/2  =( 9-2x²)/2 .

   b) x+2 /(x+2)² * x²-4 / x = 1/(x+2) *( x+2)(x-2)/x =(x-2)/x

  c) [ ( 2/x +1/x+1) ÷ ( x-1/x+1 )]*x = [ (2x+2+x/x(x+1))÷(x²+x-1/x+1)]*x

     =[ 3x+2/x(x+1)*(x+1)/(x²+x-1)]*x= ( 3x+2)/(x²+x-1)

    6.simplifica:

    a) (3+x)²/(3+x)(3-x)*x²(3-x)/x²(3+x) / 2(x-2)/1 * (x-2)/2(x-2)²= 1

    b) (x+3)(x+2)/(x-4)(x-1)*(x-2)/(x+2)(x-2) +x(x-2)/x(x-4)=

     =(x+3)(x-2)+(x-1)(x-2)(x-2)/(x-4)(x-1)(x-2) =

     = (x-2)( x+3 +(x-1)(x-2))/(x-4)(x-1)(x-2) =( x+3+(x-1)(x-2))/ (x-4)(x-1)

    c) ( x +1)(x-1)/(x+2) +3(x-1)/(x+3) -(x-3)/(x+3)(x+2)=

       = ( x+3)(x+1)(x-1) +3(x-1)(x+2)-(x-3)/(x+2)(x+3)

       = x³-x+3x²-3+3x²+3x-6-x+3/(x+2)(x+3)= x³+6x²+x-6/(x+2)(x+3)

     d) ( x+2)(x+1)/(x+2)/(x+2)(x+1) = (x+1)/(x+2)(x+1)= 1/(x+2).