Vereinfachen (Kürzen) gebrochen rationaler Funktionen
Diese Seite generiert bei jedem Neuladen per Zufall 20 gebrochen rationale Funktionsterme, die noch nicht vollständig
gekürzt sind. Zur Übung kannst du dir ein paar Blätter ausdrucken und jeweils die rechte Seite abdecken oder
abschneiden. Dort steht die vollständig faktorisierte sowie am Schluss die vollständig gekürzte Form des Funktionsterms.
(Natürlich müsste man, wenn man genau ist, die Definitionslücken der Funktion am Anfang
bestimmen, bevor man kürzt.)
|
| 1) |
-5x6+45x4 |
= |
|
= |
-5x4(x+3)(x-3) |
= |
-5x2(x+3) |
| 2x4-12x3+18x2 |
2x2(x-3)2 |
2(x-3) |
|
| 2) |
4x3-4x |
= |
|
= |
4x(x+1)(x-1) |
= |
(x+1) |
| 4x3-8x2+4x |
4x(x-1)2 |
(x-1) |
|
| 3) |
-3x5-9x4 |
= |
|
= |
-3x4(x+3) |
= |
x4 |
| -3x4+54x2-243 |
-3(x+3)2(x-3)2 |
(x+3)(x-3)2 |
|
| 4) |
4x2-2x-12 |
= |
|
= |
2(x-2)(2x+3) |
= |
2(2x+3) |
| 3x4-12x3+12x2 |
3x2(x-2)2 |
3x2(x-2) |
|
| 5) |
x3-4x |
= |
|
= |
x(x+2)(x-2) |
= |
-(x+2)(x-2) |
| -32x6+80x5-50x4 |
-2x4(4x-5)2 |
2x3(4x-5)2 |
|
| 6) |
-2x7+6x6+18x5-54x4 |
= |
|
= |
-2x4(x+3)(x-3)2 |
= |
2x4(x+3) |
| -x2+6x-9 |
-(x-3)2 |
|
| 7) |
22x3+99x2+132x+44 |
= |
|
= |
11(x+2)2(2x+1) |
= |
11(2x+1) |
| 4x4-32x2+64 |
4(x+2)2(x-2)2 |
4(x-2)2 |
|
| 8) |
x5-4x4+4x3 |
= |
|
= |
x3(x-2)2 |
= |
x2(x-2)2 |
| 3x3+12x2+12x |
3x(x+2)2 |
3(x+2)2 |
|
| 9) |
3x3-3x2-3x+3 |
= |
|
= |
3(x+1)(x-1)2 |
= |
-3(x+1)(x-1) |
| -11x+11 |
-11(x-1) |
11 |
|
| 10) |
22x2-26x+4 |
= |
|
= |
2(x-1)(11x-2) |
= |
2 |
| 77x4-91x3+14x2 |
7x2(x-1)(11x-2) |
7x2 |
|
| 11) |
5x2+20x+20 |
= |
|
= |
5(x+2)2 |
= |
-5 |
| -x8-2x7+4x6+8x5 |
-x5(x+2)2(x-2) |
x5(x-2) |
|
| 12) |
-5x4+10x3+20x2-40x |
= |
|
= |
-5x(x+2)(x-2)2 |
= |
-5(x+2)(x-2) |
| 16x6-52x5+40x4 |
4x4(x-2)(4x-5) |
4x3(4x-5) |
|
| 13) |
-x4+x2 |
= |
|
= |
-x2(x+1)(x-1) |
= |
-x2(x-1) |
| x2+2x+1 |
(x+1)2 |
(x+1) |
|
| 14) |
-2x-2 |
= |
|
= |
-2(x+1) |
= |
-(x+1) |
| 2x2-4x+2 |
2(x-1)2 |
(x-1)2 |
|
| 15) |
-x6+3x5 |
= |
|
= |
-x5(x-3) |
= |
x5 |
| -20x3+5x2+180x-45 |
-5(x+3)(x-3)(4x-1) |
5(x+3)(4x-1) |
|
| 16) |
-3x4-9x3+27x2+81x |
= |
|
= |
-3x(x+3)2(x-3) |
= |
3 |
| -5x6+90x4-405x2 |
-5x2(x+3)2(x-3)2 |
5x(x-3) |
|
| 17) |
x2+2x+1 |
= |
|
= |
(x+1)2 |
= |
-(x+1)2 |
| -343x4-441x3-189x2-27x |
-x(7x+3)3 |
x(7x+3)3 |
|
| 18) |
-30x+10 |
= |
|
= |
-10(3x-1) |
= |
-5(3x-1) |
| 4x2-8x+4 |
4(x-1)2 |
2(x-1)2 |
|
| 19) |
-2x5+4x3-2x |
= |
|
= |
-2x(x+1)2(x-1)2 |
= |
2x |
| -x4+2x2-1 |
-(x+1)2(x-1)2 |
|
| 20) |
5x4-90x2+405 |
= |
|
= |
5(x+3)2(x-3)2 |
= |
-5(x+3)(x-3) |
| -2x6+18x4 |
-2x4(x+3)(x-3) |
2x4 |
|