Whakaoti i te F(x)=5x^2-(x+7/x^3-x

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

Whakaoti mō F

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

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te x\left(x-1\right)\left(x+1\right).

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

Whakareatia te x ki te x, ka x^{2}.

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

Whakamahia te āhuatanga tohatoha hei whakarea te Fx^{2} ki te x-1.

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

Whakamahia te āhuatanga tuaritanga hei whakarea te Fx^{3}-Fx^{2} ki te x+1 ka whakakotahi i ngā kupu rite.

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

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 2 me te 1 kia riro ai te 3.

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

Whakamahia te āhuatanga tohatoha hei whakarea te 5x^{3} ki te x-1.

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

Whakamahia te āhuatanga tuaritanga hei whakarea te 5x^{4}-5x^{3} ki te x+1 ka whakakotahi i ngā kupu rite.

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

Hei kimi i te tauaro o x+7, kimihia te tauaro o ia taurangi.

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

Pahekotia ngā kīanga tau katoa e whai ana i te F.

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

Whakawehea ngā taha e rua ki te x^{4}-x^{2}.

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

Mā te whakawehe ki te x^{4}-x^{2} ka wetekia te whakareanga ki te x^{4}-x^{2}.

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

Whakawehe 5x^{5}-5x^{3}-x-7 ki te x^{4}-x^{2}.

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