Issolvi y=p(x-1)+4/x

$$y = p ( x - 1 ) + \frac { 4 } { x }$$

Solvi għal p (complex solution)

$$\left\{\begin{matrix}p=-\frac{4-xy}{x\left(x-1\right)}\text{, }&x\neq 1\text{ and }x\neq 0\\p\in \mathrm{C}\text{, }&x=1\text{ and }y=4\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'x.

$$yx=p\left(x-1\right)x+4$$

Uża l-propjetà distributtiva biex timmultiplika p b'x-1.

$$yx=\left(px-p\right)x+4$$

Uża l-propjetà distributtiva biex timmultiplika px-p b'x.

$$yx=px^{2}-px+4$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$px^{2}-px+4=yx$$

Naqqas 4 miż-żewġ naħat.

$$px^{2}-px=yx-4$$

Ikkombina t-termini kollha li fihom p.

$$\left(x^{2}-x\right)p=yx-4$$

L-ekwazzjoni hija f'forma standard.

$$\left(x^{2}-x\right)p=xy-4$$

Iddividi ż-żewġ naħat b'x^{2}-x.

$$\frac{\left(x^{2}-x\right)p}{x^{2}-x}=\frac{xy-4}{x^{2}-x}$$

Meta tiddividi b'x^{2}-x titneħħa l-multiplikazzjoni b'x^{2}-x.

$$p=\frac{xy-4}{x^{2}-x}$$

Iddividi yx-4 b'x^{2}-x.

$$p=\frac{xy-4}{x\left(x-1\right)}$$

Solvi għal p

$$\left\{\begin{matrix}p=-\frac{4-xy}{x\left(x-1\right)}\text{, }&x\neq 1\text{ and }x\neq 0\\p\in \mathrm{R}\text{, }&x=1\text{ and }y=4\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'x.

$$yx=p\left(x-1\right)x+4$$

Uża l-propjetà distributtiva biex timmultiplika p b'x-1.

$$yx=\left(px-p\right)x+4$$

Uża l-propjetà distributtiva biex timmultiplika px-p b'x.

$$yx=px^{2}-px+4$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$px^{2}-px+4=yx$$

Naqqas 4 miż-żewġ naħat.

$$px^{2}-px=yx-4$$

Ikkombina t-termini kollha li fihom p.

$$\left(x^{2}-x\right)p=yx-4$$

L-ekwazzjoni hija f'forma standard.

$$\left(x^{2}-x\right)p=xy-4$$

Iddividi ż-żewġ naħat b'x^{2}-x.

$$\frac{\left(x^{2}-x\right)p}{x^{2}-x}=\frac{xy-4}{x^{2}-x}$$

Meta tiddividi b'x^{2}-x titneħħa l-multiplikazzjoni b'x^{2}-x.

$$p=\frac{xy-4}{x^{2}-x}$$

Iddividi yx-4 b'x^{2}-x.

$$p=\frac{xy-4}{x\left(x-1\right)}$$

Solvi għal x (complex solution)

$$\left\{\begin{matrix}x=-\frac{\sqrt{y^{2}+2py+p^{2}-16p}-p-y}{2p}\text{; }x=\frac{\sqrt{y^{2}+2py+p^{2}-16p}+p+y}{2p}\text{, }&p\neq 0\\x=\frac{4}{y}\text{, }&p=0\text{ and }y\neq 0\end{matrix}\right.$$

Solvi għal x

$$\left\{\begin{matrix}x=-\frac{\sqrt{y^{2}+2py+p^{2}-16p}-p-y}{2p}\text{; }x=\frac{\sqrt{y^{2}+2py+p^{2}-16p}+p+y}{2p}\text{, }&p\neq 0\text{ and }\left(y\geq -p+4\sqrt{p}\text{ or }y\leq -p-4\sqrt{p}\text{ or }p<0\right)\\x=\frac{4}{y}\text{, }&p=0\text{ and }y\neq 0\end{matrix}\right.$$