CAPITULO XIII
Reducción de fracciones
Reducción de fracciones
Reducir una fracción a expresión entera o mixta
- Ejercicio 123
Reducir a expresión entera o mixta:
-
6
a
3
–10
a
2
2a
6 a 3 –10 a 2 2a = a 3 2a – a 2 2a =3 a 2 –5a -
9
x
2
y–6
x
2
y
2
+3x
y
3
3xy
9 x 2 y–6 x 2 y 2 +3x y 3 3xy = x 2 y 3xy – x 2 y 2 3xy + 3x y 3 3xy =3x–2xy+ y 2 -
x
2
+3
x
x 2 +3 x = x 2 x + 3 x =x+ 3 x -
10
a
2
+15a–2
5a
2a+3– 2 5a
-
9
x
3
–6
x
2
+3x–5
3x
3 x 2 –2x+1– 5 3x
-
x
2
–5x–16
x+2
x–7– 2 x+2
-
12
x
2
–6x–2
4x–1
3x– 3 4 – 11 4 4x–1 =3x– 3 4 – 11 4( 4x–1 ) =3x– 3( 4x–1 ) +11 4( 4x–1 ) =3x– 12x–3+11 4( 4x–1 ) =3x– 12x+8 4( 4x–1 ) =3x– 4 ( 3x+2 ) 4 ( 4x–1 ) =3x– 3x+2 4x–1 -
a
3
+3
b
3
a+2b
a 2 –2ab+4 b 2 – 5 b 3 a+2b
-
x
3
–
x
2
–6x+1
x
2
–3
x–1– 3x+2 x 2 –3
-
3
x
3
+4
x
2
y+2x
y
2
–6
y
3
3x–2y
x 2 +2xy+2 y 2 – 2 y 3 3x–2y
-
2
x
3
–7
x
2
+6x–8
2
x
2
–x+1
x–3+ 2x–5 2 x 2 –x+1
-
2
a
4
–3
a
3
+
a
2
a
2
–a+1
2 a 2 –a–2– a–2 a 2 –a+1
-
x
4
–4
x
2
–3x
x
2
–2
x 2 –2– 3x+4 x 2 –2
-
10
n
3
–18
n
2
–5n+3
2
n
2
–3n+1
5n– 3 2 + – 29 2 n+ 9 2 2 n 2 –3n+1 =5n– 3 2 + 9–29n 2 2 n 2 –3n+1 =5n– 3 2 + –29n+9 2( 2 n 2 –3n+1 ) =5n– 1 2 ( 3– 9–29n 2 n 2 –3n+1 ) =5n– 1 2 ( 6 n 2 –9n+3–9+29n 2 n 2 –3n+1 ) =5n– 1 2 ( 6 n 2 +20n–6 2 n 2 –3n+1 ) =5n– 1 2 [ 2 ( 3 n 2 +10n–3 ) 2 n 2 –3n+1 ] =5n– 3 n 2 +10n–3 2 n 2 –3n+1 -
8
x
4
4
x
2
+5x+6
2 x 2 – 5 2 x+ 1 8 + 115 8 x– 3 4 4 x 2 +5x+6 =2 x 2 – 5 2 x+ 1 8 + 115x–6 8 4 x 2 +5x+6 =2 x 2 – 5 2 x+ 1 8 + 115x–6 8( 4 x 2 +5x+6 ) =2 x 2 – 1 2 [ 5x– 1 4 – 115x–6 4( 4 x 2 +5x+6 ) ] =2 x 2 – 1 2 [ 20x( 4 x 2 +5x+6 ) –( 4 x 2 +5x+6 ) –115x+6 4( 4 x 2 +5x+6 ) ] =2 x 2 – 1 2 [ 80 x 3 +100 x 2 + 120x –4 x 2 – 5x – 6 – 115x + 6 4( 4 x 2 +5x+6 ) ] =2 x 2 – 1 2 [ 80 x 3 +96 x 2 4( 4 x 2 +5x+6 ) ] =2 x 2 – 1 2 [ 8 ( 10 x 3 +12 x 2 ) 4 ( 4 x 2 +5x+6 ) ] =2 x 2 – 10 x 3 +12 x 2 4 x 2 +5x+6
-
6
m
5
+3
m
4
n
3
m
3
–m
n
2
+
n
3
2 m 2 +mn+ 2 3 n 2 + – m 2 n 3 – 1 3 m n 4 – 2 3 n 5 3 m 3 –m n 2 + n 3 =2 m 2 +mn+ 2 3 n 2 + –3 m 2 n 3 –m n 4 –2 n 5 3 3 m 3 –m n 2 + n 3 =2 m 2 +mn+ 2 3 n 2 + –3 m 2 n 3 –m n 4 –2 n 5 3( 3 m 3 –m n 2 + n 3 ) =2 m 2 +mn+ 1 3 [ 2 n 2 + –3 m 2 n 3 –m n 4 –2 n 5 3 m 3 –m n 2 + n 3 ] =2 m 2 +mn+ 1 3 [ 2 n 2 ( 3 m 3 –m n 2 + n 3 ) –3 m 2 n 3 –m n 4 –2 n 5 3 m 3 –m n 2 + n 3 ] =2 m 2 +mn+ 1 3 [ 6 m 3 n 2 –2m n 4 + 2 n 5 –3 m 2 n 3 –m n 4 – 2 n 5 3 m 3 –m n 2 + n 3 ] =2 m 2 +mn+ 1 3 [ 6 m 3 n 2 –3 m 2 n 3 –3m n 4 3 m 3 –m n 2 + n 3 ] =2 m 2 +mn+ 1 3 [ 3 ( 2 m 3 n 2 – m 2 n 3 –m n 4 ) 3 m 3 –m n 2 + n 3 ] =2 m 2 +mn+ 2 m 3 n 2 – m 2 n 3 –m n 4 3 m 3 –m n 2 + n 3
