Whakaoti i te (x+1/x)^2-(x-1/x)^2

$$( x + \frac { 1 } { x } ) ^ { 2 } - ( x - \frac { 1 } { x } ) ^ { 2 }$$

Aromātai

$$4$$

Ngā Hipanga Rongoā Poto

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x ki te \frac{x}{x}.

$$\left(\frac{xx}{x}+\frac{1}{x}\right)^{2}-\left(x-\frac{1}{x}\right)^{2}$$

Tā te mea he rite te tauraro o \frac{xx}{x} me \frac{1}{x}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\left(\frac{xx+1}{x}\right)^{2}-\left(x-\frac{1}{x}\right)^{2}$$

Mahia ngā whakarea i roto o xx+1.

$$\left(\frac{x^{2}+1}{x}\right)^{2}-\left(x-\frac{1}{x}\right)^{2}$$

Kia whakarewa i te \frac{x^{2}+1}{x} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$\frac{\left(x^{2}+1\right)^{2}}{x^{2}}-\left(x-\frac{1}{x}\right)^{2}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia x ki te \frac{x}{x}.

$$\frac{\left(x^{2}+1\right)^{2}}{x^{2}}-\left(\frac{xx}{x}-\frac{1}{x}\right)^{2}$$

Tā te mea he rite te tauraro o \frac{xx}{x} me \frac{1}{x}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\left(x^{2}+1\right)^{2}}{x^{2}}-\left(\frac{xx-1}{x}\right)^{2}$$

Mahia ngā whakarea i roto o xx-1.

$$\frac{\left(x^{2}+1\right)^{2}}{x^{2}}-\left(\frac{x^{2}-1}{x}\right)^{2}$$

Kia whakarewa i te \frac{x^{2}-1}{x} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$\frac{\left(x^{2}+1\right)^{2}}{x^{2}}-\frac{\left(x^{2}-1\right)^{2}}{x^{2}}$$

Tā te mea he rite te tauraro o \frac{\left(x^{2}+1\right)^{2}}{x^{2}} me \frac{\left(x^{2}-1\right)^{2}}{x^{2}}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\left(x^{2}+1\right)^{2}-\left(x^{2}-1\right)^{2}}{x^{2}}$$

Mahia ngā whakarea i roto o \left(x^{2}+1\right)^{2}-\left(x^{2}-1\right)^{2}.

$$\frac{x^{4}+2x^{2}+1-x^{4}+2x^{2}-1}{x^{2}}$$

Whakakotahitia ngā kupu rite i x^{4}+2x^{2}+1-x^{4}+2x^{2}-1.

$$\frac{4x^{2}}{x^{2}}$$

Me whakakore tahi te x^{2} i te taurunga me te tauraro.

$$4$$

Tauwehe

$$2^{2}$$