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Testar genererad Latex.

$\hspace{8} 2x+4={{6} \over {x}}$

$2x+4-{{6} \over {x}}=0$

$\hspace{8} -{{6} \over {x}}+2x+4=0$

$\hspace{8} -{{6} \over {x}}+2x+4=0$

Common denominator: $x$
$-6/x+2x+4 = (-6+2x^2+4x)/x$
$\hspace{8} {{-6+2x^2+4x} \over {x}}=0$

Common factor $2$
$\hspace{8} {{2x^2+4x-6} \over {x}}=0$

Zero factor method: Solve $2x^2+4x-6=0$
$\hspace{8} 2x^2+4x-6=0$

Common factor $2$
Common factor $2$
$\hspace{8} x^2+2x-3=0$

Quadratic formula: $x^2+2x-3 \Leftrightarrow (x+3)(x-1)$
$\hspace{8} (x+3)(x-1)=0$

Zero factor method: Solve $x+3=0$
$\hspace{8} x+3=0$

$x+3$ gives root $x=-3$
Zero factor method: Solve $x-1=0$
$\hspace{8} x-1=0$

$x-1$ gives root $x=1$

$\hspace{8} 2x+4={{6} \over {x}}$

$\hspace{8} 2x+4-{{6} \over {x}}=0$

$\hspace{8} -{{6} \over {x}}+2x+4=0$

Gemensam nämnare: $x$
$-6/x+2x+4 = (-6+2x^2+4x)/x$
$\hspace{8} {{-6+2x^2+4x} \over {x}}=0$

$\hspace{8} {{2x^2+4x-6} \over {x}}=0$

Nollproduduktsmetoden: lös $2x^2+4x-6=0$
$\hspace{8} 2x^2+4x-6=0$

$\hspace{8} {{2x^2} \over {2}}+{{4x} \over {2}}-{{6} \over {2}}=0$

$\hspace{8} x^2+2x-3=0$

PQ-formeln: $x^2+2x-3 \Leftrightarrow (x+3)(x-1)$
$\hspace{8} (x+3)(x-1)=0$

Nollproduduktsmetoden: lös $x+3=0$
$\hspace{8} x+3=0$

$x+3$ ger rot $x=-3$
Nollproduduktsmetoden: lös $x-1=0$

$\hspace{8} x-1=0$

$x-1$ ger rot $x=1$

$2x+4=6/x$ har lösningen $x_{1}=1$, $x_{2}=-3$

 

Division med over: $12\cdot{x\over 12}$

Division med frac: $12\cdot\frac{x}{12}$

Division med dfrac: $12\cdot\dfrac{x}{12}$

Lösning 1

$\hspace{7em} \left\{\begin{array}{lr}3x+2y=39.1\\7y+4x=94.6\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}x=\dfrac{-2y+39.1}{3}\\7y+4x=94.6\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}x=\dfrac{-2y+39.1}{3}\\7y+4 \cdot \dfrac{-2y+39.1}{3}=94.6\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}x=\dfrac{-2y+39.1}{3}\\y=9.8\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}x=\dfrac{-2 \cdot 9.8+39.1}{3}\\y=9.8\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}x=6.5\\y=9.8\end{array}\right.$

Lösning 2

$\hspace{7em} \left\{\begin{array}{lr}3x+2y=39.1\\7y+4x=94.6\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}y=\dfrac{-3x+39.1}{2}\\7y+4x=94.6\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}y=\dfrac{-3x+39.1}{2}\\7 \cdot \dfrac{-3x+39.1}{2}+4x=94.6\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}y=\dfrac{-3x+39.1}{2}\\x=6.5\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}y=\dfrac{-3 \cdot 6.5+39.1}{2}\\x=6.5\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}y=9.8\\x=6.5\end{array}\right.$

Lösning 3

$\hspace{7em} \left\{\begin{array}{lr}3x+2y=39.1\\7y+4x=94.6\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}3x+2y=39.1\\x=\dfrac{-7y+94.6}{4}\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}3 \cdot \dfrac{-7y+94.6}{4}+2y=39.1\\x=\dfrac{-7y+94.6}{4}\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}y=9.8\\x=\dfrac{-7y+94.6}{4}\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}y=9.8\\x=\dfrac{-7 \cdot 9.8+94.6}{4}\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}y=9.8\\x=6.5\end{array}\right.$

Lösning 4

$\hspace{7em} \left\{\begin{array}{lr}3x+2y=39.1\\7y+4x=94.6\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}3x+2y=39.1\\y=\dfrac{-4x+94.6}{7}\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}3x+2 \cdot \dfrac{-4x+94.6}{7}=39.1\\y=\dfrac{-4x+94.6}{7}\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}x=6.5\\y=\dfrac{-4x+94.6}{7}\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}x=6.5\\y=\dfrac{-4 \cdot 6.5+94.6}{7}\end{array}\right.$

$\hspace{7em} \left\{\begin{array}{lr}x=6.5\\y=9.8\end{array}\right.$