Revision history for MatheGKL1
Additions:
= (3/(√2-1))* (√2+1/√2+1)
= (3*√2+3)/(2-1)
=3*√2+3
= (3*√2+3)/(2-1)
=3*√2+3
Deletions:
Additions:
{{image url="vereinfachen4.jpg" width="100" class="left"}}
Deletions:
Additions:
√27/(√6-√3) = √(3*9)/(√(2*3)-√3) =
{{image url="vereinfachen4.jpg" width="70" class="left"}}
{{image url="vereinfachen4.jpg" width="70" class="left"}}
Additions:
= x³+y³/x+y
**e)**
**e)**
Additions:
{{image url="vereinfachen3.jpg" width="70" class="left"}}
Deletions:
Additions:
**d)**
(x²/y + y²/x)/(1/x + 1/y) =
{{image url="vereinfachen3.jpg" width="350" class="left"}}
(x²/y + y²/x)/(1/x + 1/y) =
{{image url="vereinfachen3.jpg" width="350" class="left"}}
Additions:
**c)**
(x+y/x-y) + (x-y/ x+y)
= ((x+y)² + (x-y)²)/((x-y)*(x+y))
= (x² + 2xy + y² + x² - 2xy + y²)/x²-y²
= (2x² + 2y²)/ (x²-y²)
(x+y/x-y) + (x-y/ x+y)
= ((x+y)² + (x-y)²)/((x-y)*(x+y))
= (x² + 2xy + y² + x² - 2xy + y²)/x²-y²
= (2x² + 2y²)/ (x²-y²)
Deletions:
Additions:
**0.1.4.T**
1/xy + 1/xz + 1/yz
= z/xyz + y/xyz + x/xyz
= (x+y+z)* 1/xyz
**b**
(u/v - v/u)*(u/v+v/u) = (u²+v²/uv)
= (1/(uv)²)* (u²-v²)* (u²+v²)
= (1/(uv)²)* (u^4-v^4)
1/xy + 1/xz + 1/yz
= z/xyz + y/xyz + x/xyz
= (x+y+z)* 1/xyz
**b**
(u/v - v/u)*(u/v+v/u) = (u²+v²/uv)
= (1/(uv)²)* (u²-v²)* (u²+v²)
= (1/(uv)²)* (u^4-v^4)
Additions:
**Berechnen Sie ohne Taschenrechner (erst möglichst viel kürzen, Primfaktorzerlegung!)**
**a)**
**umstellen nach R1:**
**b)**
Rp = 1/(1/R1 + 1/R2 + 1/R3)
1/Rp = 1/R1 + 1/R2 + 1/R3
1/R1 = 1/Rp - 1/R2 - 1/R3 =
(R2R3 - RpR3 - RpR2) / RpR2R3
R1 = (RpR2R3)/ R2R3 - RpR3 - RpR2
**a)**
**umstellen nach R1:**
**b)**
Rp = 1/(1/R1 + 1/R2 + 1/R3)
1/Rp = 1/R1 + 1/R2 + 1/R3
1/R1 = 1/Rp - 1/R2 - 1/R3 =
(R2R3 - RpR3 - RpR2) / RpR2R3
R1 = (RpR2R3)/ R2R3 - RpR3 - RpR2
Deletions:
a)
umstellen nach R1:
Additions:
= (0,12*30*10^-6*8*10^3)/(10^-4*5^2*2^-2)
= (12*3*8*4)/5^2
= ((3*2^2*3*2^3*2^2)/5^2)* (2^2/2^2)
= (2^9*9)/100 = 5,12*9 = 46,08 1/cm
**Fassen Sie auf einen gemeinsamen Nenner zusammen, beseitigen Sie ggf. Mehrfachbrüche und machen Sie ggf. den Nenner rational**
**0.1.3.T**
a)
Rp = 1/(1/R1 + 1/R2)
(1/Rp)* (R1R2/R1R2) = (1/R1)*(RpR2/RpR2)+1/R2*(RpR2/RpR2)
R1R2/RpR1R2 = RpR2/RpR1R2 + RpR1/RpR1R2
R1R2 = RpR2 + RpR1
umstellen nach R1:
R1R2 - RpR1 = RpR2
R1(R2-Rp) = RpR2
R1 = (Rp*R2)/(R2-Rp)
= (12*3*8*4)/5^2
= ((3*2^2*3*2^3*2^2)/5^2)* (2^2/2^2)
= (2^9*9)/100 = 5,12*9 = 46,08 1/cm
**Fassen Sie auf einen gemeinsamen Nenner zusammen, beseitigen Sie ggf. Mehrfachbrüche und machen Sie ggf. den Nenner rational**
**0.1.3.T**
a)
Rp = 1/(1/R1 + 1/R2)
(1/Rp)* (R1R2/R1R2) = (1/R1)*(RpR2/RpR2)+1/R2*(RpR2/RpR2)
R1R2/RpR1R2 = RpR2/RpR1R2 + RpR1/RpR1R2
R1R2 = RpR2 + RpR1
umstellen nach R1:
R1R2 - RpR1 = RpR2
R1(R2-Rp) = RpR2
R1 = (Rp*R2)/(R2-Rp)
Additions:
{{image url="vereinfachen2.jpg" width="350" class="left"}}
Deletions:
Additions:
**0.1.2.T**
B =
{{image url="vereinfachen2.jpg" width="300" class="left"}}
B =
{{image url="vereinfachen2.jpg" width="300" class="left"}}
Additions:
A =(5^3*3^2*2^2*3^2*2^11*3)/(2^4*3^4*2^3*5^3*2^6*3^3*2^3*2)
A =1/(2^4*3^2)
= 1/(4*3)^2
=1/144
A =1/(2^4*3^2)
= 1/(4*3)^2
=1/144
No Differences
Additions:
||
Berechnen Sie ohne Taschenrechner (erst möglichst viel kürzen, Primfaktorzerlegung!)
**0.1.1.T**
A =
{{image url="vereinfachen1.jpg" width="300" class="left"}}
||
Berechnen Sie ohne Taschenrechner (erst möglichst viel kürzen, Primfaktorzerlegung!)
**0.1.1.T**
A =
{{image url="vereinfachen1.jpg" width="300" class="left"}}
||
Additions:
{{files}}
Deletions:
{{image url="MatheGKL12.jpg" width="650" class="center"}}
{{image url="MatheGKL13.jpg" width="650" class="center"}}
Additions:
===Umformen und Vereinfachen Mathematischer Terme - Lösungen===
Deletions:
Deletions:
Additions:
===Mathematische Therme - Lösungen===
{{image url="MatheGKL11.jpg" width="650" class="center"}}
{{image url="MatheGKL12.jpg" width="650" class="center"}}
{{image url="MatheGKL13.jpg" width="650" class="center"}}
||**{{files download="MatheGKL1.pdf"text="PDF Dokument Lösungen Mathematische Terme"}}**||
{{image url="MatheGKL11.jpg" width="650" class="center"}}
{{image url="MatheGKL12.jpg" width="650" class="center"}}
{{image url="MatheGKL13.jpg" width="650" class="center"}}
||**{{files download="MatheGKL1.pdf"text="PDF Dokument Lösungen Mathematische Terme"}}**||
Deletions:
{{image url="MatheGKL1.jpg" width="650" class="center"}}
||**{{files download="MatheGKL1.pdf"text="PDF Dokument Aufgaben Mathematische Terme"}}**||
