MA0001/Exercise 1/tasks/3.tex

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\begin{deloppgaver}
\delo
\begin{alignat*}{4}
& 1^{-1} &&+ 2^{-1} &&+ 3^{-1} \\[1ex]
& \frac{1}{1} &&+ \frac{1}{2} &&+ \frac{1}{3} \\[2ex]
& \frac{6}{6} &&+ \frac{3}{6} &&+ \frac{2}{6} & \qquad \text{Største felles divisor er 6} \\[2ex]
& \frac{11}{6} \\
\end{alignat*}
\delo
\begin{align*}
& x^{-7} x^{6} \\
& x^{-7+6} \\
& x^{-1} \\
& \frac{1}{x}
\end{align*}
\delo
\begin{align*}
& \frac{ \left ( x^2 y z^3 \right )^2 }{ x^4 y^3 z^5 } \\[2ex]
& \frac{ x^4 y^2 z^6 }{ x^4 y^3 z^5 } \\[2ex]
& x^{4-4} y^{2-3} z^{6-5} \\
& x^0 y^{-1} z^1 \\[2ex]
& \frac{z}{y} \\
\end{align*}
\delo
\begin{align*}
& \frac{ e^{z-x} }{ e^x e^z} \\[2ex]
& \frac{ \cancel{e^z} }{ e^{x+x} \cancel{e^z} } \\[2ex]
& \frac{1}{e^{2x}} \\[2ex]
& e^{-2x}
\end{align*}
\delo
\begin{align*}
& \frac{ z^2 - y^2 }{ z+y } \\[2ex]
& \frac{ (z+y)(z-y) }{ z+y } && \text{3. Kvadratsetning} \\[2ex]
& \frac{ \cancel{(z+y)}(z-y) }{ \cancel{z+y} } \\[2ex]
& z-y
\end{align*}
\end{deloppgaver}