Datrys 3/2x+1-1/3x+2=2g

$$\frac { 3 } { 2 x + 1 } - \frac { 1 } { 3 x + 2 } = 2 g$$

Datrys ar gyfer g

$$g=\frac{7x+5}{2\left(6x^{2}+7x+2\right)}$$

$$x\neq -\frac{1}{2}\text{ and }x\neq -\frac{2}{3}$$

Camau ar gyfer Datrys Hafaliad Llinol

Lluoswch ddwy ochr yr hafaliad wrth \left(2x+1\right)\left(3x+2\right), lluoswm cyffredin lleiaf 2x+1,3x+2.

$$\left(3x+2\right)\times 3-\left(2x+1\right)=2g\left(2x+1\right)\left(3x+2\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi 3x+2 â 3.

$$9x+6-\left(2x+1\right)=2g\left(2x+1\right)\left(3x+2\right)$$

I ddod o hyd i wrthwyneb 2x+1, dewch o hyd i wrthwyneb pob term.

$$9x+6-2x-1=2g\left(2x+1\right)\left(3x+2\right)$$

Cyfuno 9x a -2x i gael 7x.

$$7x+6-1=2g\left(2x+1\right)\left(3x+2\right)$$

Tynnu 1 o 6 i gael 5.

$$7x+5=2g\left(2x+1\right)\left(3x+2\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi 2g â 2x+1.

$$7x+5=\left(4xg+2g\right)\left(3x+2\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi 4xg+2g â 3x+2 a chyfuno termau tebyg.

$$7x+5=12gx^{2}+14gx+4g$$

Cyfnewidiwch yr ochrau fel bod yr holl dermau newidiol ar yr ochr chwith.

$$12gx^{2}+14gx+4g=7x+5$$

Cyfuno pob term sy'n cynnwys g.

$$\left(12x^{2}+14x+4\right)g=7x+5$$

Rhannu’r ddwy ochr â 12x^{2}+14x+4.

$$\frac{\left(12x^{2}+14x+4\right)g}{12x^{2}+14x+4}=\frac{7x+5}{12x^{2}+14x+4}$$

Mae rhannu â 12x^{2}+14x+4 yn dad-wneud lluosi â 12x^{2}+14x+4.

$$g=\frac{7x+5}{12x^{2}+14x+4}$$

Rhannwch 7x+5 â 12x^{2}+14x+4.

$$g=\frac{7x+5}{2\left(6x^{2}+7x+2\right)}$$

Datrys ar gyfer x (complex solution)

$$\left\{\begin{matrix}x=-\frac{\sqrt{4g^{2}+44g+49}+14g-7}{24g}\text{; }x=-\frac{-\sqrt{4g^{2}+44g+49}+14g-7}{24g}\text{, }&g\neq 0\\x=-\frac{5}{7}\text{, }&g=0\end{matrix}\right.$$

Datrys ar gyfer x

$$\left\{\begin{matrix}x=-\frac{\sqrt{4g^{2}+44g+49}+14g-7}{24g}\text{; }x=-\frac{-\sqrt{4g^{2}+44g+49}+14g-7}{24g}\text{, }&g\leq -3\sqrt{2}-\frac{11}{2}\text{ or }\left(g\neq 0\text{ and }g\geq 3\sqrt{2}-\frac{11}{2}\right)\\x=-\frac{5}{7}\text{, }&g=0\end{matrix}\right.$$