Matemáticas Académicas
www.aulamatematica.com
010. 









44
3496
2
2
2
2
xx
xx
:
xx
xx
:
12
65
2
2


xx
xx
x2
– 6x + 9 = (x – 3)2
x2
– x = x (x – 1)
Factorizamos los que no se pueden hacer mentalmente:
Método I: x2
– 4x + 3
1 – 4 3
3 3 – 3
1 – 1 0
(x – 3) (x – 1)
Método II: x2
– 4x + 3
x =
12
314164
·
··
=
2
44 
=
2
24 
=





1
3
2
1
x
x
(x – 3) (x – 1)
x2
– 4x + 4 = (x – 2)2
Método I : x2
– 5x + 6
1 – 5 6
3 3 – 6
1 – 2 0
(x – 3) (x – 2)
x2
– 2x + 1 = (x – 1)2
= 









2
2
2
31
1
3
)x(
)x)(x(
:
)x(x
)x(
: 2
1
32
)x(
)x)(x(


=
=
)x(x
)x(
1
3 2


·
)x)(x(
)x(
31
2 2


·
)x)(x(
)x(
32
1 2


=
=
x
x 2
012.
1
1
2
2


x
)a(
:
2
2
1
1
)x(
a


=
)x)(x(
)a(
11
1 2


·
)a)(a(
)x(
11
1 2


=
)a)(x(
)x)·(a(
11
11


014. 





 2
2 11
xx
xx : 






x
x
1
1
2
34
1
x
xxx 
:
x
xx 12

=
Factorizamos y sustituimos:
x4
– x3
+ x – 1
1 – 1 0 1 – 1
1 1 0 0 1
1 0 0 1 0
 Marta Martín Sierra
Fracciones algebraicas
– 1 – 1 1 – 1
1 – 1 1 0
(x – 1) (x + 1) (x2
– x + 1)
= 2
2
111
x
)xx)(x)(x( 
·
12
 xx
x
=
=
x
)x)(x( 11 
015. 







 2
1
2
1
1
x
x
x






1
1
x
= 







 )x)(x(
x
x 11
2
1
1
· 




 
x
x1
=
= 







)x)(x(
xx
11
21
·
x
x1
=
=
)x)(x(
x


11
1
·
x
x1
=
=
x
1
017. 2
44
)yx(
yx


·
xyx
yx


2
Factorizamos: x4
– y4
= (x2
)2
– (y2
)2
=
= (x2
+ y2
)· (x2
– y2
) =
= (x2
+ y2
) (x + y) (x – y)
= 2
22
)yx(
)yx)(yx)·(yx(


·
)yx(x
yx


· 22
yx
x

= 1
018. (x + 1)











1
1
1
2
2
x
x
)x(
= (x + 1)










)x)(x(
)x)(x)(x()x(
11
1111 2
=
(opcional)=
 










))((
))()(()()(
11
11111 2
xx
xxxxx
=
=










1
1121 22
x
)x)(x(xx
=
=
1
121 232


x
xxxxx
=
=
1
23


x
xx

Fracciones algeb mixto_blog

  • 1.
    Matemáticas Académicas www.aulamatematica.com 010.           44 3496 2 2 2 2 xx xx : xx xx : 12 65 2 2   xx xx x2 –6x + 9 = (x – 3)2 x2 – x = x (x – 1) Factorizamos los que no se pueden hacer mentalmente: Método I: x2 – 4x + 3 1 – 4 3 3 3 – 3 1 – 1 0 (x – 3) (x – 1) Método II: x2 – 4x + 3 x = 12 314164 · ·· = 2 44  = 2 24  =      1 3 2 1 x x (x – 3) (x – 1) x2 – 4x + 4 = (x – 2)2 Método I : x2 – 5x + 6 1 – 5 6 3 3 – 6 1 – 2 0 (x – 3) (x – 2) x2 – 2x + 1 = (x – 1)2 =           2 2 2 31 1 3 )x( )x)(x( : )x(x )x( : 2 1 32 )x( )x)(x(   = = )x(x )x( 1 3 2   · )x)(x( )x( 31 2 2   · )x)(x( )x( 32 1 2   = = x x 2 012. 1 1 2 2   x )a( : 2 2 1 1 )x( a   = )x)(x( )a( 11 1 2   · )a)(a( )x( 11 1 2   = )a)(x( )x)·(a( 11 11   014.        2 2 11 xx xx :        x x 1 1 2 34 1 x xxx  : x xx 12  = Factorizamos y sustituimos: x4 – x3 + x – 1 1 – 1 0 1 – 1 1 1 0 0 1 1 0 0 1 0
  • 2.
     Marta MartínSierra Fracciones algebraicas – 1 – 1 1 – 1 1 – 1 1 0 (x – 1) (x + 1) (x2 – x + 1) = 2 2 111 x )xx)(x)(x(  · 12  xx x = = x )x)(x( 11  015.          2 1 2 1 1 x x x       1 1 x =          )x)(x( x x 11 2 1 1 ·        x x1 = =         )x)(x( xx 11 21 · x x1 = = )x)(x( x   11 1 · x x1 = = x 1 017. 2 44 )yx( yx   · xyx yx   2 Factorizamos: x4 – y4 = (x2 )2 – (y2 )2 = = (x2 + y2 )· (x2 – y2 ) = = (x2 + y2 ) (x + y) (x – y) = 2 22 )yx( )yx)(yx)·(yx(   · )yx(x yx   · 22 yx x  = 1 018. (x + 1)            1 1 1 2 2 x x )x( = (x + 1)           )x)(x( )x)(x)(x()x( 11 1111 2 = (opcional)=             ))(( ))()(()()( 11 11111 2 xx xxxxx = =           1 1121 22 x )x)(x(xx = = 1 121 232   x xxxxx = = 1 23   x xx