Datrys {l}{7x+2/2x-3+5x+4/x=34x^2+43x-2/4x^2-9+10-x/2x^2-3x}{y=333}{text{Solvefor}ztext{where}}{z=y}

$$\left. \begin{array} { l } { \frac{7 x + 2}{2 x - 3} + \frac{5 x + 4}{x} = \frac{34 x ^ {2} + 43 x - 2}{4 x ^ {2} - 9} + \frac{10 - x}{2 x ^ {2} - 3 x} }\\ { y = 333 }\\ { \text{Solve for } z \text{ where} } \\ { z = y } \end{array} \right.$$

Datrys ar gyfer x, y, z

$$z=333$$

Camau Ateb

Ystyriwch yr hafaliad cyntaf. All y newidyn x ddim fod yn hafal i unrhyw un o’r gwerthoedd -\frac{3}{2},0,\frac{3}{2} gan nad ydy rhannu â sero wedi’i ddiffinio. Lluoswch ddwy ochr yr hafaliad wrth x\left(2x-3\right)\left(2x+3\right), lluoswm cyffredin lleiaf 2x-3,x,4x^{2}-9,2x^{2}-3x.

$$x\left(2x+3\right)\left(7x+2\right)+\left(4x^{2}-9\right)\left(5x+4\right)=x\left(34x^{2}+43x-2\right)+\left(2x+3\right)\left(10-x\right)$$

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

$$\left(2x^{2}+3x\right)\left(7x+2\right)+\left(4x^{2}-9\right)\left(5x+4\right)=x\left(34x^{2}+43x-2\right)+\left(2x+3\right)\left(10-x\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi 2x^{2}+3x â 7x+2 a chyfuno termau tebyg.

$$14x^{3}+25x^{2}+6x+\left(4x^{2}-9\right)\left(5x+4\right)=x\left(34x^{2}+43x-2\right)+\left(2x+3\right)\left(10-x\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi 4x^{2}-9 â 5x+4.

$$14x^{3}+25x^{2}+6x+20x^{3}+16x^{2}-45x-36=x\left(34x^{2}+43x-2\right)+\left(2x+3\right)\left(10-x\right)$$

Cyfuno 14x^{3} a 20x^{3} i gael 34x^{3}.

$$34x^{3}+25x^{2}+6x+16x^{2}-45x-36=x\left(34x^{2}+43x-2\right)+\left(2x+3\right)\left(10-x\right)$$

Cyfuno 25x^{2} a 16x^{2} i gael 41x^{2}.

$$34x^{3}+41x^{2}+6x-45x-36=x\left(34x^{2}+43x-2\right)+\left(2x+3\right)\left(10-x\right)$$

Cyfuno 6x a -45x i gael -39x.

$$34x^{3}+41x^{2}-39x-36=x\left(34x^{2}+43x-2\right)+\left(2x+3\right)\left(10-x\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi x â 34x^{2}+43x-2.

$$34x^{3}+41x^{2}-39x-36=34x^{3}+43x^{2}-2x+\left(2x+3\right)\left(10-x\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi 2x+3 â 10-x a chyfuno termau tebyg.

$$34x^{3}+41x^{2}-39x-36=34x^{3}+43x^{2}-2x+17x-2x^{2}+30$$

Cyfuno -2x a 17x i gael 15x.

$$34x^{3}+41x^{2}-39x-36=34x^{3}+43x^{2}+15x-2x^{2}+30$$

Cyfuno 43x^{2} a -2x^{2} i gael 41x^{2}.

$$34x^{3}+41x^{2}-39x-36=34x^{3}+41x^{2}+15x+30$$

Tynnu 34x^{3} o'r ddwy ochr.

$$34x^{3}+41x^{2}-39x-36-34x^{3}=41x^{2}+15x+30$$

Cyfuno 34x^{3} a -34x^{3} i gael 0.

$$41x^{2}-39x-36=41x^{2}+15x+30$$

Tynnu 41x^{2} o'r ddwy ochr.

$$41x^{2}-39x-36-41x^{2}=15x+30$$

Cyfuno 41x^{2} a -41x^{2} i gael 0.

$$-39x-36=15x+30$$

Tynnu 15x o'r ddwy ochr.

$$-39x-36-15x=30$$

Cyfuno -39x a -15x i gael -54x.

$$-54x-36=30$$

Ychwanegu 36 at y ddwy ochr.

$$-54x=30+36$$

Adio 30 a 36 i gael 66.

$$-54x=66$$

Rhannu’r ddwy ochr â -54.

$$x=\frac{66}{-54}$$

Lleihau'r ffracsiwn \frac{66}{-54} i'r graddau lleiaf posib drwy dynnu a chanslo allan 6.

$$x=-\frac{11}{9}$$

Mae’r system wedi’i datrys nawr.

$$x=-\frac{11}{9} y=333 z=333$$