Resolver m(x)=x^2-6x+8/x^2+5x-14,w

$$m ( x ) = \frac { x ^ { 2 } - 6 x + 8 } { x ^ { 2 } + 5 x - 14 } , w$$

Ebatzi: m

$$m=-\frac{4-x}{x\left(x+7\right)}$$

$$x\neq -7\text{ and }x\neq 0\text{ and }x\neq 2$$

Ekuazio lineala ebazteko urratsak

Biderkatu ekuazioaren bi aldeak honekin: \left(x-2\right)\left(x+7\right).

$$mx\left(x-2\right)\left(x+7\right)=x^{2}-6x+8$$

Erabili banaketa-propietatea mx eta x-2 biderkatzeko.

$$\left(mx^{2}-2mx\right)\left(x+7\right)=x^{2}-6x+8$$

Erabili banaketa-propietatea mx^{2}-2mx eta x+7 biderkatzeko eta antzeko gaiak bateratzeko.

$$mx^{3}+5mx^{2}-14mx=x^{2}-6x+8$$

Konbinatu m duten gai guztiak.

$$\left(x^{3}+5x^{2}-14x\right)m=x^{2}-6x+8$$

Zatitu ekuazioaren bi aldeak x^{3}+5x^{2}-14x balioarekin.

$$\frac{\left(x^{3}+5x^{2}-14x\right)m}{x^{3}+5x^{2}-14x}=\frac{\left(x-4\right)\left(x-2\right)}{x^{3}+5x^{2}-14x}$$

x^{3}+5x^{2}-14x balioarekin zatituz gero, x^{3}+5x^{2}-14x balioarekiko biderketa desegiten da.

$$m=\frac{\left(x-4\right)\left(x-2\right)}{x^{3}+5x^{2}-14x}$$

Zatitu \left(-4+x\right)\left(-2+x\right) balioa x^{3}+5x^{2}-14x balioarekin.

$$m=\frac{x-4}{x\left(x+7\right)}$$

Ebatzi: x (complex solution)

$$\left\{\begin{matrix}x=\frac{-\sqrt{49m^{2}-30m+1}-7m+1}{2m}\text{, }&m\neq 0\text{ and }m\neq -\frac{1}{9}\\x=\frac{\sqrt{49m^{2}-30m+1}-7m+1}{2m}\text{, }&m\neq 0\\x=4\text{, }&m=0\end{matrix}\right.$$

Ebatzi: x

$$\left\{\begin{matrix}x=\frac{-\sqrt{49m^{2}-30m+1}-7m+1}{2m}\text{, }&\left(m\neq -\frac{1}{9}\text{ and }m\neq 0\text{ and }m\leq \frac{15-4\sqrt{11}}{49}\right)\text{ or }m\geq \frac{4\sqrt{11}+15}{49}\\x=\frac{\sqrt{49m^{2}-30m+1}-7m+1}{2m}\text{, }&\left(m\neq 0\text{ and }m\leq \frac{15-4\sqrt{11}}{49}\right)\text{ or }m\geq \frac{4\sqrt{11}+15}{49}\\x=4\text{, }&m=0\end{matrix}\right.$$