Whakaoti i te 5/6x+18+x+9/2x

$$\frac { 5 } { 6 x + 18 } + \frac { x + 9 } { 2 x }$$

Aromātai

$$\frac{3x^{2}+41x+81}{6x\left(x+3\right)}$$

Ngā Hipanga Rongoā Poto

Tauwehea te 6x+18.

$$\frac{5}{6\left(x+3\right)}+\frac{x+9}{2x}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 6\left(x+3\right) me 2x ko 6x\left(x+3\right). Whakareatia \frac{5}{6\left(x+3\right)} ki te \frac{x}{x}. Whakareatia \frac{x+9}{2x} ki te \frac{3\left(x+3\right)}{3\left(x+3\right)}.

$$\frac{5x}{6x\left(x+3\right)}+\frac{\left(x+9\right)\times 3\left(x+3\right)}{6x\left(x+3\right)}$$

Tā te mea he rite te tauraro o \frac{5x}{6x\left(x+3\right)} me \frac{\left(x+9\right)\times 3\left(x+3\right)}{6x\left(x+3\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{5x+\left(x+9\right)\times 3\left(x+3\right)}{6x\left(x+3\right)}$$

Mahia ngā whakarea i roto o 5x+\left(x+9\right)\times 3\left(x+3\right).

$$\frac{5x+3x^{2}+9x+27x+81}{6x\left(x+3\right)}$$

Whakakotahitia ngā kupu rite i 5x+3x^{2}+9x+27x+81.

$$\frac{41x+3x^{2}+81}{6x\left(x+3\right)}$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{41x+3x^{2}+81}{6x\left(x+3\right)}.

$$\frac{3\left(x-\left(-\frac{1}{6}\sqrt{709}-\frac{41}{6}\right)\right)\left(x-\left(\frac{1}{6}\sqrt{709}-\frac{41}{6}\right)\right)}{6x\left(x+3\right)}$$

Me whakakore tahi te 3 i te taurunga me te tauraro.

$$\frac{\left(x-\left(-\frac{1}{6}\sqrt{709}-\frac{41}{6}\right)\right)\left(x-\left(\frac{1}{6}\sqrt{709}-\frac{41}{6}\right)\right)}{2x\left(x+3\right)}$$

Whakarohaina te 2x\left(x+3\right).

$$\frac{\left(x-\left(-\frac{1}{6}\sqrt{709}-\frac{41}{6}\right)\right)\left(x-\left(\frac{1}{6}\sqrt{709}-\frac{41}{6}\right)\right)}{2x^{2}+6x}$$

Hei kimi i te tauaro o -\frac{1}{6}\sqrt{709}-\frac{41}{6}, kimihia te tauaro o ia taurangi.

$$\frac{\left(x-\left(-\frac{1}{6}\sqrt{709}\right)-\left(-\frac{41}{6}\right)\right)\left(x-\left(\frac{1}{6}\sqrt{709}-\frac{41}{6}\right)\right)}{2x^{2}+6x}$$

Ko te tauaro o -\frac{1}{6}\sqrt{709} ko \frac{1}{6}\sqrt{709}.

$$\frac{\left(x+\frac{1}{6}\sqrt{709}-\left(-\frac{41}{6}\right)\right)\left(x-\left(\frac{1}{6}\sqrt{709}-\frac{41}{6}\right)\right)}{2x^{2}+6x}$$

Ko te tauaro o -\frac{41}{6} ko \frac{41}{6}.

$$\frac{\left(x+\frac{1}{6}\sqrt{709}+\frac{41}{6}\right)\left(x-\left(\frac{1}{6}\sqrt{709}-\frac{41}{6}\right)\right)}{2x^{2}+6x}$$

Hei kimi i te tauaro o \frac{1}{6}\sqrt{709}-\frac{41}{6}, kimihia te tauaro o ia taurangi.

$$\frac{\left(x+\frac{1}{6}\sqrt{709}+\frac{41}{6}\right)\left(x-\frac{1}{6}\sqrt{709}-\left(-\frac{41}{6}\right)\right)}{2x^{2}+6x}$$

Ko te tauaro o -\frac{41}{6} ko \frac{41}{6}.

$$\frac{\left(x+\frac{1}{6}\sqrt{709}+\frac{41}{6}\right)\left(x-\frac{1}{6}\sqrt{709}+\frac{41}{6}\right)}{2x^{2}+6x}$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o x+\frac{1}{6}\sqrt{709}+\frac{41}{6} ki ia tau o x-\frac{1}{6}\sqrt{709}+\frac{41}{6}.

$$\frac{x^{2}+x\left(-\frac{1}{6}\right)\sqrt{709}+x\times \frac{41}{6}+\frac{1}{6}\sqrt{709}x+\frac{1}{6}\sqrt{709}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{1}{6}\sqrt{709}\times \frac{41}{6}+\frac{41}{6}x+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Whakareatia te \sqrt{709} ki te \sqrt{709}, ka 709.

$$\frac{x^{2}+x\left(-\frac{1}{6}\right)\sqrt{709}+x\times \frac{41}{6}+\frac{1}{6}\sqrt{709}x+\frac{1}{6}\times 709\left(-\frac{1}{6}\right)+\frac{1}{6}\sqrt{709}\times \frac{41}{6}+\frac{41}{6}x+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Pahekotia te x\left(-\frac{1}{6}\right)\sqrt{709} me \frac{1}{6}\sqrt{709}x, ka 0.

$$\frac{x^{2}+x\times \frac{41}{6}+\frac{1}{6}\times 709\left(-\frac{1}{6}\right)+\frac{1}{6}\sqrt{709}\times \frac{41}{6}+\frac{41}{6}x+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Whakareatia te \frac{1}{6} ki te 709, ka \frac{709}{6}.

$$\frac{x^{2}+x\times \frac{41}{6}+\frac{709}{6}\left(-\frac{1}{6}\right)+\frac{1}{6}\sqrt{709}\times \frac{41}{6}+\frac{41}{6}x+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Me whakarea te \frac{709}{6} ki te -\frac{1}{6} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{x^{2}+x\times \frac{41}{6}+\frac{709\left(-1\right)}{6\times 6}+\frac{1}{6}\sqrt{709}\times \frac{41}{6}+\frac{41}{6}x+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Mahia ngā whakarea i roto i te hautanga \frac{709\left(-1\right)}{6\times 6}.

$$\frac{x^{2}+x\times \frac{41}{6}+\frac{-709}{36}+\frac{1}{6}\sqrt{709}\times \frac{41}{6}+\frac{41}{6}x+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Ka taea te hautanga \frac{-709}{36} te tuhi anō ko -\frac{709}{36} mā te tango i te tohu tōraro.

$$\frac{x^{2}+x\times \frac{41}{6}-\frac{709}{36}+\frac{1}{6}\sqrt{709}\times \frac{41}{6}+\frac{41}{6}x+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Me whakarea te \frac{1}{6} ki te \frac{41}{6} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{x^{2}+x\times \frac{41}{6}-\frac{709}{36}+\frac{1\times 41}{6\times 6}\sqrt{709}+\frac{41}{6}x+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 41}{6\times 6}.

$$\frac{x^{2}+x\times \frac{41}{6}-\frac{709}{36}+\frac{41}{36}\sqrt{709}+\frac{41}{6}x+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Pahekotia te x\times \frac{41}{6} me \frac{41}{6}x, ka \frac{41}{3}x.

$$\frac{x^{2}+\frac{41}{3}x-\frac{709}{36}+\frac{41}{36}\sqrt{709}+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Me whakarea te \frac{41}{6} ki te -\frac{1}{6} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{x^{2}+\frac{41}{3}x-\frac{709}{36}+\frac{41}{36}\sqrt{709}+\frac{41\left(-1\right)}{6\times 6}\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Mahia ngā whakarea i roto i te hautanga \frac{41\left(-1\right)}{6\times 6}.

$$\frac{x^{2}+\frac{41}{3}x-\frac{709}{36}+\frac{41}{36}\sqrt{709}+\frac{-41}{36}\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Ka taea te hautanga \frac{-41}{36} te tuhi anō ko -\frac{41}{36} mā te tango i te tohu tōraro.

$$\frac{x^{2}+\frac{41}{3}x-\frac{709}{36}+\frac{41}{36}\sqrt{709}-\frac{41}{36}\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Pahekotia te \frac{41}{36}\sqrt{709} me -\frac{41}{36}\sqrt{709}, ka 0.

$$\frac{x^{2}+\frac{41}{3}x-\frac{709}{36}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Me whakarea te \frac{41}{6} ki te \frac{41}{6} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{x^{2}+\frac{41}{3}x-\frac{709}{36}+\frac{41\times 41}{6\times 6}}{2x^{2}+6x}$$

Mahia ngā whakarea i roto i te hautanga \frac{41\times 41}{6\times 6}.

$$\frac{x^{2}+\frac{41}{3}x-\frac{709}{36}+\frac{1681}{36}}{2x^{2}+6x}$$

Tā te mea he rite te tauraro o -\frac{709}{36} me \frac{1681}{36}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{x^{2}+\frac{41}{3}x+\frac{-709+1681}{36}}{2x^{2}+6x}$$

Tāpirihia te -709 ki te 1681, ka 972.

$$\frac{x^{2}+\frac{41}{3}x+\frac{972}{36}}{2x^{2}+6x}$$

Whakawehea te 972 ki te 36, kia riro ko 27.

$$\frac{x^{2}+\frac{41}{3}x+27}{2x^{2}+6x}$$

Whakaroha

$$\frac{3x^{2}+41x+81}{6x\left(x+3\right)}$$

Ngā Hipanga Rongoā Poto

Tauwehea te 6x+18.

$$\frac{5}{6\left(x+3\right)}+\frac{x+9}{2x}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 6\left(x+3\right) me 2x ko 6x\left(x+3\right). Whakareatia \frac{5}{6\left(x+3\right)} ki te \frac{x}{x}. Whakareatia \frac{x+9}{2x} ki te \frac{3\left(x+3\right)}{3\left(x+3\right)}.

$$\frac{5x}{6x\left(x+3\right)}+\frac{\left(x+9\right)\times 3\left(x+3\right)}{6x\left(x+3\right)}$$

Tā te mea he rite te tauraro o \frac{5x}{6x\left(x+3\right)} me \frac{\left(x+9\right)\times 3\left(x+3\right)}{6x\left(x+3\right)}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{5x+\left(x+9\right)\times 3\left(x+3\right)}{6x\left(x+3\right)}$$

Mahia ngā whakarea i roto o 5x+\left(x+9\right)\times 3\left(x+3\right).

$$\frac{5x+3x^{2}+9x+27x+81}{6x\left(x+3\right)}$$

Whakakotahitia ngā kupu rite i 5x+3x^{2}+9x+27x+81.

$$\frac{41x+3x^{2}+81}{6x\left(x+3\right)}$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{41x+3x^{2}+81}{6x\left(x+3\right)}.

$$\frac{3\left(x-\left(-\frac{1}{6}\sqrt{709}-\frac{41}{6}\right)\right)\left(x-\left(\frac{1}{6}\sqrt{709}-\frac{41}{6}\right)\right)}{6x\left(x+3\right)}$$

Me whakakore tahi te 3 i te taurunga me te tauraro.

$$\frac{\left(x-\left(-\frac{1}{6}\sqrt{709}-\frac{41}{6}\right)\right)\left(x-\left(\frac{1}{6}\sqrt{709}-\frac{41}{6}\right)\right)}{2x\left(x+3\right)}$$

Whakarohaina te 2x\left(x+3\right).

$$\frac{\left(x-\left(-\frac{1}{6}\sqrt{709}-\frac{41}{6}\right)\right)\left(x-\left(\frac{1}{6}\sqrt{709}-\frac{41}{6}\right)\right)}{2x^{2}+6x}$$

Hei kimi i te tauaro o -\frac{1}{6}\sqrt{709}-\frac{41}{6}, kimihia te tauaro o ia taurangi.

$$\frac{\left(x-\left(-\frac{1}{6}\sqrt{709}\right)-\left(-\frac{41}{6}\right)\right)\left(x-\left(\frac{1}{6}\sqrt{709}-\frac{41}{6}\right)\right)}{2x^{2}+6x}$$

Ko te tauaro o -\frac{1}{6}\sqrt{709} ko \frac{1}{6}\sqrt{709}.

$$\frac{\left(x+\frac{1}{6}\sqrt{709}-\left(-\frac{41}{6}\right)\right)\left(x-\left(\frac{1}{6}\sqrt{709}-\frac{41}{6}\right)\right)}{2x^{2}+6x}$$

Ko te tauaro o -\frac{41}{6} ko \frac{41}{6}.

$$\frac{\left(x+\frac{1}{6}\sqrt{709}+\frac{41}{6}\right)\left(x-\left(\frac{1}{6}\sqrt{709}-\frac{41}{6}\right)\right)}{2x^{2}+6x}$$

Hei kimi i te tauaro o \frac{1}{6}\sqrt{709}-\frac{41}{6}, kimihia te tauaro o ia taurangi.

$$\frac{\left(x+\frac{1}{6}\sqrt{709}+\frac{41}{6}\right)\left(x-\frac{1}{6}\sqrt{709}-\left(-\frac{41}{6}\right)\right)}{2x^{2}+6x}$$

Ko te tauaro o -\frac{41}{6} ko \frac{41}{6}.

$$\frac{\left(x+\frac{1}{6}\sqrt{709}+\frac{41}{6}\right)\left(x-\frac{1}{6}\sqrt{709}+\frac{41}{6}\right)}{2x^{2}+6x}$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o x+\frac{1}{6}\sqrt{709}+\frac{41}{6} ki ia tau o x-\frac{1}{6}\sqrt{709}+\frac{41}{6}.

$$\frac{x^{2}+x\left(-\frac{1}{6}\right)\sqrt{709}+x\times \frac{41}{6}+\frac{1}{6}\sqrt{709}x+\frac{1}{6}\sqrt{709}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{1}{6}\sqrt{709}\times \frac{41}{6}+\frac{41}{6}x+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Whakareatia te \sqrt{709} ki te \sqrt{709}, ka 709.

$$\frac{x^{2}+x\left(-\frac{1}{6}\right)\sqrt{709}+x\times \frac{41}{6}+\frac{1}{6}\sqrt{709}x+\frac{1}{6}\times 709\left(-\frac{1}{6}\right)+\frac{1}{6}\sqrt{709}\times \frac{41}{6}+\frac{41}{6}x+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Pahekotia te x\left(-\frac{1}{6}\right)\sqrt{709} me \frac{1}{6}\sqrt{709}x, ka 0.

$$\frac{x^{2}+x\times \frac{41}{6}+\frac{1}{6}\times 709\left(-\frac{1}{6}\right)+\frac{1}{6}\sqrt{709}\times \frac{41}{6}+\frac{41}{6}x+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Whakareatia te \frac{1}{6} ki te 709, ka \frac{709}{6}.

$$\frac{x^{2}+x\times \frac{41}{6}+\frac{709}{6}\left(-\frac{1}{6}\right)+\frac{1}{6}\sqrt{709}\times \frac{41}{6}+\frac{41}{6}x+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Me whakarea te \frac{709}{6} ki te -\frac{1}{6} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{x^{2}+x\times \frac{41}{6}+\frac{709\left(-1\right)}{6\times 6}+\frac{1}{6}\sqrt{709}\times \frac{41}{6}+\frac{41}{6}x+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Mahia ngā whakarea i roto i te hautanga \frac{709\left(-1\right)}{6\times 6}.

$$\frac{x^{2}+x\times \frac{41}{6}+\frac{-709}{36}+\frac{1}{6}\sqrt{709}\times \frac{41}{6}+\frac{41}{6}x+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Ka taea te hautanga \frac{-709}{36} te tuhi anō ko -\frac{709}{36} mā te tango i te tohu tōraro.

$$\frac{x^{2}+x\times \frac{41}{6}-\frac{709}{36}+\frac{1}{6}\sqrt{709}\times \frac{41}{6}+\frac{41}{6}x+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Me whakarea te \frac{1}{6} ki te \frac{41}{6} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{x^{2}+x\times \frac{41}{6}-\frac{709}{36}+\frac{1\times 41}{6\times 6}\sqrt{709}+\frac{41}{6}x+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 41}{6\times 6}.

$$\frac{x^{2}+x\times \frac{41}{6}-\frac{709}{36}+\frac{41}{36}\sqrt{709}+\frac{41}{6}x+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Pahekotia te x\times \frac{41}{6} me \frac{41}{6}x, ka \frac{41}{3}x.

$$\frac{x^{2}+\frac{41}{3}x-\frac{709}{36}+\frac{41}{36}\sqrt{709}+\frac{41}{6}\left(-\frac{1}{6}\right)\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Me whakarea te \frac{41}{6} ki te -\frac{1}{6} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{x^{2}+\frac{41}{3}x-\frac{709}{36}+\frac{41}{36}\sqrt{709}+\frac{41\left(-1\right)}{6\times 6}\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Mahia ngā whakarea i roto i te hautanga \frac{41\left(-1\right)}{6\times 6}.

$$\frac{x^{2}+\frac{41}{3}x-\frac{709}{36}+\frac{41}{36}\sqrt{709}+\frac{-41}{36}\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Ka taea te hautanga \frac{-41}{36} te tuhi anō ko -\frac{41}{36} mā te tango i te tohu tōraro.

$$\frac{x^{2}+\frac{41}{3}x-\frac{709}{36}+\frac{41}{36}\sqrt{709}-\frac{41}{36}\sqrt{709}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Pahekotia te \frac{41}{36}\sqrt{709} me -\frac{41}{36}\sqrt{709}, ka 0.

$$\frac{x^{2}+\frac{41}{3}x-\frac{709}{36}+\frac{41}{6}\times \frac{41}{6}}{2x^{2}+6x}$$

Me whakarea te \frac{41}{6} ki te \frac{41}{6} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{x^{2}+\frac{41}{3}x-\frac{709}{36}+\frac{41\times 41}{6\times 6}}{2x^{2}+6x}$$

Mahia ngā whakarea i roto i te hautanga \frac{41\times 41}{6\times 6}.

$$\frac{x^{2}+\frac{41}{3}x-\frac{709}{36}+\frac{1681}{36}}{2x^{2}+6x}$$

Tā te mea he rite te tauraro o -\frac{709}{36} me \frac{1681}{36}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{x^{2}+\frac{41}{3}x+\frac{-709+1681}{36}}{2x^{2}+6x}$$

Tāpirihia te -709 ki te 1681, ka 972.

$$\frac{x^{2}+\frac{41}{3}x+\frac{972}{36}}{2x^{2}+6x}$$

Whakawehea te 972 ki te 36, kia riro ko 27.

$$\frac{x^{2}+\frac{41}{3}x+27}{2x^{2}+6x}$$