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

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

Resolver m

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

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

Pasos para resolver unha ecuación lineal

Multiplica ambos lados da ecuación por \left(x-2\right)\left(x+7\right).

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

Usa a propiedade distributiva para multiplicar mx por x-2.

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

Usa a propiedade distributiva para multiplicar mx^{2}-2mx por x+7 e combina os termos semellantes.

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

Combina todos os termos que conteñan m.

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

Divide ambos lados entre x^{3}+5x^{2}-14x.

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

A división entre x^{3}+5x^{2}-14x desfai a multiplicación por x^{3}+5x^{2}-14x.

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

Divide \left(-4+x\right)\left(-2+x\right) entre x^{3}+5x^{2}-14x.

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

Resolver x (complex solution)

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

Resolver x

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