Datrys F(x)=5x^2-(x+7/x^3-x

$$F ( x ) = \frac { 5 x ^ { 2 } - ( x + 7 } { x ^ { 3 } - x }$$

Datrys ar gyfer F

$$F=-\frac{7+x+5x^{3}-5x^{5}}{x^{2}\left(x^{2}-1\right)}$$

$$x\neq 0\text{ and }|x|\neq 1$$

Camau ar gyfer Datrys Hafaliad Llinol

Lluoswch ddwy ochr yr hafaliad â x\left(x-1\right)\left(x+1\right).

$$Fxx\left(x-1\right)\left(x+1\right)=5x^{2}x\left(x-1\right)\left(x+1\right)-\left(x+7\right)$$

Lluosi x a x i gael x^{2}.

$$Fx^{2}\left(x-1\right)\left(x+1\right)=5x^{2}x\left(x-1\right)\left(x+1\right)-\left(x+7\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi Fx^{2} â x-1.

$$\left(Fx^{3}-Fx^{2}\right)\left(x+1\right)=5x^{2}x\left(x-1\right)\left(x+1\right)-\left(x+7\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi Fx^{3}-Fx^{2} â x+1 a chyfuno termau tebyg.

$$Fx^{4}-Fx^{2}=5x^{2}x\left(x-1\right)\left(x+1\right)-\left(x+7\right)$$

Er mwyn lluosi pwerau sy’n rhannu’r un sail, adiwch eu esbonyddion. Adiwch 2 a 1 i gael 3.

$$Fx^{4}-Fx^{2}=5x^{3}\left(x-1\right)\left(x+1\right)-\left(x+7\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi 5x^{3} â x-1.

$$Fx^{4}-Fx^{2}=\left(5x^{4}-5x^{3}\right)\left(x+1\right)-\left(x+7\right)$$

Defnyddio’r briodwedd ddosbarthu i luosi 5x^{4}-5x^{3} â x+1 a chyfuno termau tebyg.

$$Fx^{4}-Fx^{2}=5x^{5}-5x^{3}-\left(x+7\right)$$

I ddod o hyd i wrthwyneb x+7, dewch o hyd i wrthwyneb pob term.

$$Fx^{4}-Fx^{2}=5x^{5}-5x^{3}-x-7$$

Cyfuno pob term sy'n cynnwys F.

$$\left(x^{4}-x^{2}\right)F=5x^{5}-5x^{3}-x-7$$

Rhannu’r ddwy ochr â x^{4}-x^{2}.

$$\frac{\left(x^{4}-x^{2}\right)F}{x^{4}-x^{2}}=\frac{5x^{5}-5x^{3}-x-7}{x^{4}-x^{2}}$$

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

$$F=\frac{5x^{5}-5x^{3}-x-7}{x^{4}-x^{2}}$$

Rhannwch 5x^{5}-5x^{3}-x-7 â x^{4}-x^{2}.

$$F=\frac{5x^{5}-5x^{3}-x-7}{x^{2}\left(x^{2}-1\right)}$$