Issolvi (3k+1)x^2+3k-1/(3k+1)(3k^2+8k-3)+x/9k^2-1=1/3k^2+10k+3

$$\frac { ( 3 k + 1 ) x ^ { 2 } + 3 k - 1 } { ( 3 k + 1 ) ( 3 k ^ { 2 } + 8 k - 3 ) } + \frac { x } { 9 k ^ { 2 } - 1 } = \frac { 1 } { 3 k ^ { 2 } + 10 k + 3 }$$

Solvi għal k (complex solution)

$$\left\{\begin{matrix}k=-\frac{x+3}{3x+1}\text{, }&x\neq -\frac{1}{3}\text{ and }x\neq 0\text{ and }x\neq -\frac{5}{3}\\k\in \mathrm{C}\setminus -\frac{1}{3},-3,\frac{1}{3}\text{, }&x=0\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Il-varjabbli k ma jistax ikun ugwali għal kwalunkwe mill-valuri -3,-\frac{1}{3},\frac{1}{3} billi d-diviżjoni b'żero mhix definita. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'\left(3k-1\right)\left(k+3\right)\left(3k+1\right), l-inqas denominatur komuni ta' \left(3k+1\right)\left(3k^{2}+8k-3\right),9k^{2}-1,3k^{2}+10k+3.

$$\left(3k+1\right)x^{2}+3k-1+\left(k+3\right)x=3k-1$$

Uża l-propjetà distributtiva biex timmultiplika 3k+1 b'x^{2}.

$$3kx^{2}+x^{2}+3k-1+\left(k+3\right)x=3k-1$$

Uża l-propjetà distributtiva biex timmultiplika k+3 b'x.

$$3kx^{2}+x^{2}+3k-1+kx+3x=3k-1$$

Naqqas 3k miż-żewġ naħat.

$$3kx^{2}+x^{2}+3k-1+kx+3x-3k=-1$$

Ikkombina 3k u -3k biex tikseb 0.

$$3kx^{2}+x^{2}-1+kx+3x=-1$$

Naqqas x^{2} miż-żewġ naħat.

$$3kx^{2}-1+kx+3x=-1-x^{2}$$

Żid 1 maż-żewġ naħat.

$$3kx^{2}+kx+3x=-1-x^{2}+1$$

Żid -1 u 1 biex tikseb 0.

$$3kx^{2}+kx+3x=-x^{2}$$

Naqqas 3x miż-żewġ naħat.

$$3kx^{2}+kx=-x^{2}-3x$$

Ikkombina t-termini kollha li fihom k.

$$\left(3x^{2}+x\right)k=-x^{2}-3x$$

Iddividi ż-żewġ naħat b'3x^{2}+x.

$$\frac{\left(3x^{2}+x\right)k}{3x^{2}+x}=-\frac{x\left(x+3\right)}{3x^{2}+x}$$

Meta tiddividi b'3x^{2}+x titneħħa l-multiplikazzjoni b'3x^{2}+x.

$$k=-\frac{x\left(x+3\right)}{3x^{2}+x}$$

Iddividi -x\left(3+x\right) b'3x^{2}+x.

$$k=-\frac{x+3}{3x+1}$$

Il-varjabbli k ma tistax tkun ugwali għal kwalunkwe mill-valuri -\frac{1}{3},-3,\frac{1}{3}.

$$k=-\frac{x+3}{3x+1}\text{, }k\neq -\frac{1}{3}\text{ and }k\neq -3\text{ and }k\neq \frac{1}{3}$$

Solvi għal k

$$\left\{\begin{matrix}k=-\frac{x+3}{3x+1}\text{, }&x\neq -\frac{1}{3}\text{ and }x\neq -\frac{5}{3}\text{ and }x\neq 0\\k\in \mathrm{R}\setminus -\frac{1}{3},\frac{1}{3},-3\text{, }&x=0\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Il-varjabbli k ma jistax ikun ugwali għal kwalunkwe mill-valuri -3,-\frac{1}{3},\frac{1}{3} billi d-diviżjoni b'żero mhix definita. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'\left(3k-1\right)\left(k+3\right)\left(3k+1\right), l-inqas denominatur komuni ta' \left(3k+1\right)\left(3k^{2}+8k-3\right),9k^{2}-1,3k^{2}+10k+3.

$$\left(3k+1\right)x^{2}+3k-1+\left(k+3\right)x=3k-1$$

Uża l-propjetà distributtiva biex timmultiplika 3k+1 b'x^{2}.

$$3kx^{2}+x^{2}+3k-1+\left(k+3\right)x=3k-1$$

Uża l-propjetà distributtiva biex timmultiplika k+3 b'x.

$$3kx^{2}+x^{2}+3k-1+kx+3x=3k-1$$

Naqqas 3k miż-żewġ naħat.

$$3kx^{2}+x^{2}+3k-1+kx+3x-3k=-1$$

Ikkombina 3k u -3k biex tikseb 0.

$$3kx^{2}+x^{2}-1+kx+3x=-1$$

Naqqas x^{2} miż-żewġ naħat.

$$3kx^{2}-1+kx+3x=-1-x^{2}$$

Żid 1 maż-żewġ naħat.

$$3kx^{2}+kx+3x=-1-x^{2}+1$$

Żid -1 u 1 biex tikseb 0.

$$3kx^{2}+kx+3x=-x^{2}$$

Naqqas 3x miż-żewġ naħat.

$$3kx^{2}+kx=-x^{2}-3x$$

Ikkombina t-termini kollha li fihom k.

$$\left(3x^{2}+x\right)k=-x^{2}-3x$$

Iddividi ż-żewġ naħat b'3x^{2}+x.

$$\frac{\left(3x^{2}+x\right)k}{3x^{2}+x}=-\frac{x\left(x+3\right)}{3x^{2}+x}$$

Meta tiddividi b'3x^{2}+x titneħħa l-multiplikazzjoni b'3x^{2}+x.

$$k=-\frac{x\left(x+3\right)}{3x^{2}+x}$$

Iddividi -x\left(3+x\right) b'3x^{2}+x.

$$k=-\frac{x+3}{3x+1}$$

Il-varjabbli k ma tistax tkun ugwali għal kwalunkwe mill-valuri -\frac{1}{3},-3,\frac{1}{3}.

$$k=-\frac{x+3}{3x+1}\text{, }k\neq -\frac{1}{3}\text{ and }k\neq -3\text{ and }k\neq \frac{1}{3}$$

Solvi għal x (complex solution)

$$x=-\frac{k+3}{3k+1}$$

$$x=0\text{, }k\neq -\frac{1}{3}\text{ and }k\neq -3\text{ and }k\neq \frac{1}{3}$$

Solvi għal x

$$x=-\frac{k+3}{3k+1}$$

$$x=0\text{, }k\neq -3\text{ and }|k|\neq \frac{1}{3}$$