COCIENTES NOTABLES: son de tres tipos
1._ ![\frac{ x^{4} -1}{1+ x^{2} } \frac{ x^{4} -1}{1+ x^{2} }](https://tex.z-dn.net/?f=+%5Cfrac%7B+x%5E%7B4%7D+-1%7D%7B1%2B+x%5E%7B2%7D+%7D+)
2._ ![\frac{8m ^{3 }+ n^{6} }{2m+n ^{2} } \frac{8m ^{3 }+ n^{6} }{2m+n ^{2} }](https://tex.z-dn.net/?f=+%5Cfrac%7B8m+%5E%7B3+%7D%2B+n%5E%7B6%7D++%7D%7B2m%2Bn+%5E%7B2%7D+%7D+)
3._ ![\frac{1- a^{5} }{1-a} \frac{1- a^{5} }{1-a}](https://tex.z-dn.net/?f=+%5Cfrac%7B1-+a%5E%7B5%7D+%7D%7B1-a%7D+)
4._ ![\frac{ x^{6}-27 y^{3} }{ x^{2} -3y} \frac{ x^{6}-27 y^{3} }{ x^{2} -3y}](https://tex.z-dn.net/?f=+%5Cfrac%7B+x%5E%7B6%7D-27+y%5E%7B3%7D++%7D%7B+x%5E%7B2%7D+-3y%7D+)
5._ ![\frac{ x^{6}-49 y^{6} }{ x^{3}+7 y^{3} } \frac{ x^{6}-49 y^{6} }{ x^{3}+7 y^{3} }](https://tex.z-dn.net/?f=+%5Cfrac%7B+x%5E%7B6%7D-49+y%5E%7B6%7D+%7D%7B+x%5E%7B3%7D%2B7+y%5E%7B3%7D++%7D+)
6._ ![\frac{ a^{14} - b^{14} }{ a^{2}- b^{2} } \frac{ a^{14} - b^{14} }{ a^{2}- b^{2} }](https://tex.z-dn.net/?f=+%5Cfrac%7B+a%5E%7B14%7D+-+b%5E%7B14%7D+%7D%7B+a%5E%7B2%7D-+b%5E%7B2%7D++%7D+)
7._ ![\frac{1+ a^{3} }{1+a} \frac{1+ a^{3} }{1+a}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%2B+a%5E%7B3%7D+%7D%7B1%2Ba%7D+)
8._ ![\frac{16 x^{2} y^{4} -25 m^{6} }{4x y^{2} +5 m^{3} } \frac{16 x^{2} y^{4} -25 m^{6} }{4x y^{2} +5 m^{3} }](https://tex.z-dn.net/?f=+%5Cfrac%7B16+x%5E%7B2%7D++y%5E%7B4%7D+-25+m%5E%7B6%7D+%7D%7B4x+y%5E%7B2%7D+%2B5+m%5E%7B3%7D+%7D+)
9._ ![\frac{ x^{27}+ y^{27} }{ x^{3} +y^{3} } \frac{ x^{27}+ y^{27} }{ x^{3} +y^{3} }](https://tex.z-dn.net/?f=+%5Cfrac%7B+x%5E%7B27%7D%2B+y%5E%7B27%7D+%7D%7B+x%5E%7B3%7D++%2By%5E%7B3%7D+%7D+)
10._ ![\frac{ a^{27}+ y^{27} }{ a^{9} + y^{9} } \frac{ a^{27}+ y^{27} }{ a^{9} + y^{9} }](https://tex.z-dn.net/?f=+%5Cfrac%7B+a%5E%7B27%7D%2B+y%5E%7B27%7D++%7D%7B+a%5E%7B9%7D+%2B+y%5E%7B9%7D+%7D+)
11._ ![\frac{ a^{4} b^{4}-64 x^{6} }{ a^{2} b^{2} +8 x^{3}} \frac{ a^{4} b^{4}-64 x^{6} }{ a^{2} b^{2} +8 x^{3}}](https://tex.z-dn.net/?f=+%5Cfrac%7B+a%5E%7B4%7D+b%5E%7B4%7D-64+x%5E%7B6%7D+%7D%7B+a%5E%7B2%7D+b%5E%7B2%7D+%2B8+x%5E%7B3%7D%7D+)
12._![\frac{1- a^{2} b^{4} c^{8}}{1-a b^{2} c^{4}} \frac{1- a^{2} b^{4} c^{8}}{1-a b^{2} c^{4}}](https://tex.z-dn.net/?f=+%5Cfrac%7B1-+a%5E%7B2%7D+b%5E%7B4%7D+c%5E%7B8%7D%7D%7B1-a+b%5E%7B2%7D+c%5E%7B4%7D%7D+)
13._ ![\frac{32 x^{5}+243 y^{5} }{2x+3y} \frac{32 x^{5}+243 y^{5} }{2x+3y}](https://tex.z-dn.net/?f=+%5Cfrac%7B32+x%5E%7B5%7D%2B243+y%5E%7B5%7D+%7D%7B2x%2B3y%7D+)
14._ ![\frac{25-(a+1) ^{2} }{5+(a+1)} \frac{25-(a+1) ^{2} }{5+(a+1)}](https://tex.z-dn.net/?f=+%5Cfrac%7B25-%28a%2B1%29+%5E%7B2%7D+%7D%7B5%2B%28a%2B1%29%7D+)
15._ ![\frac{1- x^{12} }{1- x^{4} } \frac{1- x^{12} }{1- x^{4} }](https://tex.z-dn.net/?f=+%5Cfrac%7B1-+x%5E%7B12%7D+%7D%7B1-+x%5E%7B4%7D+%7D+)
16._ ![\frac{64 x^{6}-343 y^{9} }{4 x^{2}-7 y^{3} } \frac{64 x^{6}-343 y^{9} }{4 x^{2}-7 y^{3} }](https://tex.z-dn.net/?f=+%5Cfrac%7B64+x%5E%7B6%7D-343+y%5E%7B9%7D++%7D%7B4+x%5E%7B2%7D-7+y%5E%7B3%7D++%7D+)
17._ ![\frac{ a^{18} - b^{18} }{ a^{3}+ b^{3} } \frac{ a^{18} - b^{18} }{ a^{3}+ b^{3} }](https://tex.z-dn.net/?f=+%5Cfrac%7B+a%5E%7B18%7D+-+b%5E%7B18%7D+%7D%7B+a%5E%7B3%7D%2B+b%5E%7B3%7D++%7D+)
18._ ![\frac{(a+x) ^{2}- y^{2} }{(a+x)-y} \frac{(a+x) ^{2}- y^{2} }{(a+x)-y}](https://tex.z-dn.net/?f=+%5Cfrac%7B%28a%2Bx%29+%5E%7B2%7D-+y%5E%7B2%7D++%7D%7B%28a%2Bx%29-y%7D+)
19._ ![\frac{1+ x^{11} }{x+1} \frac{1+ x^{11} }{x+1}](https://tex.z-dn.net/?f=+%5Cfrac%7B1%2B+x%5E%7B11%7D+%7D%7Bx%2B1%7D+)
20._ ![\frac{ x^{40} - y^{40} }{ x^{8}- y^{8} } \frac{ x^{40} - y^{40} }{ x^{8}- y^{8} }](https://tex.z-dn.net/?f=+%5Cfrac%7B+x%5E%7B40%7D+-+y%5E%7B40%7D+%7D%7B+x%5E%7B8%7D-+y%5E%7B8%7D++%7D+)
21._ ![\frac{9-36 x^{10} }{3+6 x^{5} } \frac{9-36 x^{10} }{3+6 x^{5} }](https://tex.z-dn.net/?f=+%5Cfrac%7B9-36+x%5E%7B10%7D+%7D%7B3%2B6+x%5E%7B5%7D+%7D+)
22._ ![\frac{ x^{8}-256 }{x-2} \frac{ x^{8}-256 }{x-2}](https://tex.z-dn.net/?f=+%5Cfrac%7B+x%5E%7B8%7D-256+%7D%7Bx-2%7D+)
angiemontenegr:
Cuanto hago? Son muchos
Respuestas
Respuesta dada por:
6
1)
x⁴ - 1 / 1 +x² = (x² +1)( x² -1)/ (x² +1) simplificamos = x² -1 = ( x+1)( x -1)
2)
8m³ + n⁶ / 2m +n² = 2³m³ +n⁶ / 2m +n² = ( 2m + n²) ((2m)² - (2m)(n²) +(n²)² / (2m +n²) =
(2m + n²)(4m² - 2mn² + n⁴)/(2m +n²) simplificamos
(4m² - 2mn² +n⁴)
3)
1 +a⁵ / 1 -a = ( 1 - a)(1 +a +a²+a³+a⁴) / ( 1-a) simplifico
(1 +a +a² +a³ +a⁴)
4)
x⁶ - 27y³ / x² -3y = x⁶ - 3³y³ / (x² -3y) = ( x² - 3y)( (x²)² +(x²)(3y) +(3y)²) / ( x² -3y) =
(x² - 3y )(x⁴ +3x²y +9y²) / (x² -3y) simplificamos
(x⁴ +3x²y +9y²)
5)
x⁶ - 49y⁶ / x³ +7y³ = (x³ +7y³)( x³ - 7y³)/ (x³ +7y³) simplifico
x³ -7y³
7)
1+a³ / 1+a = (1 +a)(1 - a +a²)/ ( 1+a) simplificando
(1 - a + a²)
8)
16x²y⁴ -25m⁶ / ( 4xy² + 5m³) = (4xy² -5m³)( 4xy² + 5m³) / (4xy² +5m³) simplifico
4xy² -5m³
x⁴ - 1 / 1 +x² = (x² +1)( x² -1)/ (x² +1) simplificamos = x² -1 = ( x+1)( x -1)
2)
8m³ + n⁶ / 2m +n² = 2³m³ +n⁶ / 2m +n² = ( 2m + n²) ((2m)² - (2m)(n²) +(n²)² / (2m +n²) =
(2m + n²)(4m² - 2mn² + n⁴)/(2m +n²) simplificamos
(4m² - 2mn² +n⁴)
3)
1 +a⁵ / 1 -a = ( 1 - a)(1 +a +a²+a³+a⁴) / ( 1-a) simplifico
(1 +a +a² +a³ +a⁴)
4)
x⁶ - 27y³ / x² -3y = x⁶ - 3³y³ / (x² -3y) = ( x² - 3y)( (x²)² +(x²)(3y) +(3y)²) / ( x² -3y) =
(x² - 3y )(x⁴ +3x²y +9y²) / (x² -3y) simplificamos
(x⁴ +3x²y +9y²)
5)
x⁶ - 49y⁶ / x³ +7y³ = (x³ +7y³)( x³ - 7y³)/ (x³ +7y³) simplifico
x³ -7y³
7)
1+a³ / 1+a = (1 +a)(1 - a +a²)/ ( 1+a) simplificando
(1 - a + a²)
8)
16x²y⁴ -25m⁶ / ( 4xy² + 5m³) = (4xy² -5m³)( 4xy² + 5m³) / (4xy² +5m³) simplifico
4xy² -5m³
Respuesta dada por:
4
Te dejo la solución en archivo adjunto
Espero que te sirva, salu2!!!!
Espero que te sirva, salu2!!!!
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