Réitigh 30x*(y+20-x)/(3x+5)y(20-x)=6*(x+5)/3x+5

$$\frac{ 30x \times (y+20-x) }{ (3x+5)y(20-x) } = \frac{ 6 \times (x+5) }{ 3x+5 }$$

Réitigh do y.

$$y=-\frac{5x\left(20-x\right)}{x^{2}-10x-100}$$

$$x\neq 20\text{ and }x\neq 0\text{ and }x\neq 5\sqrt{5}+5\text{ and }x\neq 5-5\sqrt{5}\text{ and }x\neq -\frac{5}{3}$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Ní féidir leis an athróg y a bheith comhionann le 0 toisc nach bhfuil an roinnt faoi nialas sainithe. Iolraigh an dá thaobh den chothromóid faoi y\left(x-20\right)\left(3x+5\right), an comhiolraí is lú de \left(3x+5\right)y\left(20-x\right),3x+5.

$$-30x\left(y+20-x\right)=y\left(x-20\right)\times 6\left(x+5\right)$$

Úsáid an t-airí dáileach chun -30x a mhéadú faoi y+20-x.

$$-30xy-600x+30x^{2}=y\left(x-20\right)\times 6\left(x+5\right)$$

Úsáid an t-airí dáileach chun y a mhéadú faoi x-20.

$$-30xy-600x+30x^{2}=\left(yx-20y\right)\times 6\left(x+5\right)$$

Úsáid an t-airí dáileach chun yx-20y a mhéadú faoi 6.

$$-30xy-600x+30x^{2}=\left(6yx-120y\right)\left(x+5\right)$$

Úsáid an t-airí dáileach chun 6yx-120y a mhéadú faoi x+5 agus chun téarmaí comhchosúla a chumasc.

$$-30xy-600x+30x^{2}=6yx^{2}-90yx-600y$$

Bain 6yx^{2} ón dá thaobh.

$$-30xy-600x+30x^{2}-6yx^{2}=-90yx-600y$$

Cuir 90yx leis an dá thaobh.

$$-30xy-600x+30x^{2}-6yx^{2}+90yx=-600y$$

Cuir 600y leis an dá thaobh.

$$-30xy-600x+30x^{2}-6yx^{2}+90yx+600y=0$$

Comhcheangail -30xy agus 90yx chun 60xy a fháil.

$$60xy-600x+30x^{2}-6yx^{2}+600y=0$$

Cuir 600x leis an dá thaobh. Is ionann rud ar bith móide nialas agus a shuim féin.

$$60xy+30x^{2}-6yx^{2}+600y=600x$$

Bain 30x^{2} ón dá thaobh.

$$60xy-6yx^{2}+600y=600x-30x^{2}$$

Comhcheangail na téarmaí ar fad ina bhfuil y.

$$\left(60x-6x^{2}+600\right)y=600x-30x^{2}$$

Tá an chothromóid i bhfoirm chaighdeánach.

$$\left(600+60x-6x^{2}\right)y=600x-30x^{2}$$

Roinn an dá thaobh faoi 60x-6x^{2}+600.

$$\frac{\left(600+60x-6x^{2}\right)y}{600+60x-6x^{2}}=\frac{30x\left(20-x\right)}{600+60x-6x^{2}}$$

Má roinntear é faoi 60x-6x^{2}+600 cuirtear an iolrúchán faoi 60x-6x^{2}+600 ar ceal.

$$y=\frac{30x\left(20-x\right)}{600+60x-6x^{2}}$$

Roinn 30x\left(20-x\right) faoi 60x-6x^{2}+600.

$$y=\frac{5x\left(20-x\right)}{100+10x-x^{2}}$$

Ní féidir leis an athróg y a bheith comhionann le 0.

$$y=\frac{5x\left(20-x\right)}{100+10x-x^{2}}\text{, }y\neq 0$$

Réitigh do x.

$$\left\{\begin{matrix}x=\frac{5\left(-\sqrt{5\left(y^{2}-8y+20\right)}+y-10\right)}{y-5}\text{, }&y\neq 0\text{ and }y\neq 5\\x=\frac{5\left(\sqrt{5\left(y^{2}-8y+20\right)}+y-10\right)}{y-5}\text{, }&y\neq -\frac{65}{29}\text{ and }y\neq 5\text{ and }y\neq 0\\x=10\text{, }&y=5\end{matrix}\right.$$