Réitigh 6*x-(x+5)operatorname{npn}x=-3

$$6 \cdot x - ( x + 5 ) \operatorname { npn } x = - 3$$

Réitigh do p. (complex solution)

$$\left\{\begin{matrix}p=\frac{3\left(2x+1\right)}{x\left(x+5\right)n^{2}}\text{, }&n\neq 0\text{ and }x\neq 0\text{ and }x\neq -5\\p\in \mathrm{C}\text{, }&x=-\frac{1}{2}\text{ and }n=0\end{matrix}\right.$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Méadaigh n agus n chun n^{2} a fháil.

$$6x-\left(x+5\right)n^{2}px=-3$$

Úsáid an t-airí dáileach chun x+5 a mhéadú faoi n^{2}.

$$6x-\left(xn^{2}+5n^{2}\right)px=-3$$

Úsáid an t-airí dáileach chun xn^{2}+5n^{2} a mhéadú faoi p.

$$6x-\left(xn^{2}p+5n^{2}p\right)x=-3$$

Úsáid an t-airí dáileach chun xn^{2}p+5n^{2}p a mhéadú faoi x.

$$6x-\left(n^{2}px^{2}+5n^{2}px\right)=-3$$

Chun an mhalairt ar n^{2}px^{2}+5n^{2}px a aimsiú, aimsigh an mhalairt ar gach téarma.

$$6x-n^{2}px^{2}-5n^{2}px=-3$$

Bain 6x ón dá thaobh.

$$-n^{2}px^{2}-5n^{2}px=-3-6x$$

Comhcheangail na téarmaí ar fad ina bhfuil p.

$$\left(-n^{2}x^{2}-5n^{2}x\right)p=-3-6x$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\left(-n^{2}x^{2}-5xn^{2}\right)p=-6x-3$$

Roinn an dá thaobh faoi -5xn^{2}-x^{2}n^{2}.

$$\frac{\left(-n^{2}x^{2}-5xn^{2}\right)p}{-n^{2}x^{2}-5xn^{2}}=\frac{-6x-3}{-n^{2}x^{2}-5xn^{2}}$$

Má roinntear é faoi -5xn^{2}-x^{2}n^{2} cuirtear an iolrúchán faoi -5xn^{2}-x^{2}n^{2} ar ceal.

$$p=\frac{-6x-3}{-n^{2}x^{2}-5xn^{2}}$$

Roinn -3-6x faoi -5xn^{2}-x^{2}n^{2}.

$$p=\frac{3\left(2x+1\right)}{x\left(x+5\right)n^{2}}$$

Réitigh do p.

$$\left\{\begin{matrix}p=\frac{3\left(2x+1\right)}{x\left(x+5\right)n^{2}}\text{, }&n\neq 0\text{ and }x\neq 0\text{ and }x\neq -5\\p\in \mathrm{R}\text{, }&x=-\frac{1}{2}\text{ and }n=0\end{matrix}\right.$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Méadaigh n agus n chun n^{2} a fháil.

$$6x-\left(x+5\right)n^{2}px=-3$$

Úsáid an t-airí dáileach chun x+5 a mhéadú faoi n^{2}.

$$6x-\left(xn^{2}+5n^{2}\right)px=-3$$

Úsáid an t-airí dáileach chun xn^{2}+5n^{2} a mhéadú faoi p.

$$6x-\left(xn^{2}p+5n^{2}p\right)x=-3$$

Úsáid an t-airí dáileach chun xn^{2}p+5n^{2}p a mhéadú faoi x.

$$6x-\left(n^{2}px^{2}+5n^{2}px\right)=-3$$

Chun an mhalairt ar n^{2}px^{2}+5n^{2}px a aimsiú, aimsigh an mhalairt ar gach téarma.

$$6x-n^{2}px^{2}-5n^{2}px=-3$$

Bain 6x ón dá thaobh.

$$-n^{2}px^{2}-5n^{2}px=-3-6x$$

Comhcheangail na téarmaí ar fad ina bhfuil p.

$$\left(-n^{2}x^{2}-5n^{2}x\right)p=-3-6x$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\left(-n^{2}x^{2}-5xn^{2}\right)p=-6x-3$$

Roinn an dá thaobh faoi -5xn^{2}-x^{2}n^{2}.

$$\frac{\left(-n^{2}x^{2}-5xn^{2}\right)p}{-n^{2}x^{2}-5xn^{2}}=\frac{-6x-3}{-n^{2}x^{2}-5xn^{2}}$$

Má roinntear é faoi -5xn^{2}-x^{2}n^{2} cuirtear an iolrúchán faoi -5xn^{2}-x^{2}n^{2} ar ceal.

$$p=\frac{-6x-3}{-n^{2}x^{2}-5xn^{2}}$$

Roinn -6x-3 faoi -5xn^{2}-x^{2}n^{2}.

$$p=\frac{3\left(2x+1\right)}{x\left(x+5\right)n^{2}}$$

Réitigh do n. (complex solution)

$$\left\{\begin{matrix}n=-ip^{-\frac{1}{2}}x^{-\frac{1}{2}}\left(x+5\right)^{-\frac{1}{2}}\sqrt{-6x-3}\text{; }n=ip^{-\frac{1}{2}}x^{-\frac{1}{2}}\left(x+5\right)^{-\frac{1}{2}}\sqrt{-6x-3}\text{, }&p\neq 0\text{ and }x\neq 0\text{ and }x\neq -5\\n\in \mathrm{C}\text{, }&x=-\frac{1}{2}\text{ and }p=0\end{matrix}\right.$$

Réitigh do n.

$$\left\{\begin{matrix}n=\sqrt{\frac{3\left(2x+1\right)}{px\left(x+5\right)}}\text{; }n=-\sqrt{\frac{3\left(2x+1\right)}{px\left(x+5\right)}}\text{, }&\left(x<-5\text{ and }p<0\right)\text{ or }\left(p>0\text{ and }x>0\right)\text{ or }\left(x\geq -\frac{1}{2}\text{ and }x<0\text{ and }p<0\right)\text{ or }\left(x\leq -\frac{1}{2}\text{ and }p>0\text{ and }x>-5\right)\\n\in \mathrm{R}\text{, }&x=-\frac{1}{2}\text{ and }p=0\end{matrix}\right.$$