Datrys 5/x+1+6/x-1

$$\frac{ 5 }{ x+1 } + \frac{ 6 }{ x-1 }$$

Enrhifo

$$\frac{11x+1}{x^{2}-1}$$

Camau Ateb Byr

I ychwanegu neu dynnu mynegiannau, rhaid i chi eu ehangu i wneud eu enwaduron yr un fath. Lluosrif lleiaf cyffredin x+1 a x-1 yw \left(x-1\right)\left(x+1\right). Lluoswch \frac{5}{x+1} â \frac{x-1}{x-1}. Lluoswch \frac{6}{x-1} â \frac{x+1}{x+1}.

$$\frac{5\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}+\frac{6\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}$$

Gan fod gan \frac{5\left(x-1\right)}{\left(x-1\right)\left(x+1\right)} a \frac{6\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} yr un dynodydd, adiwch nhw drwy adio eu rhifiaduron.

$$\frac{5\left(x-1\right)+6\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}$$

Gwnewch y gwaith lluosi yn 5\left(x-1\right)+6\left(x+1\right).

$$\frac{5x-5+6x+6}{\left(x-1\right)\left(x+1\right)}$$

Cyfuno termau tebyg yn 5x-5+6x+6.

$$\frac{11x+1}{\left(x-1\right)\left(x+1\right)}$$

Ehangu \left(x-1\right)\left(x+1\right).

$$\frac{11x+1}{x^{2}-1}$$

Gwahaniaethu w.r.t. x

$$-\frac{11x^{2}+2x+11}{\left(x^{2}-1\right)^{2}}$$

Camau gan Ddefnyddio Rheol Deilliadol ar gyfer Cyniferydd

I ychwanegu neu dynnu mynegiannau, rhaid i chi eu ehangu i wneud eu enwaduron yr un fath. Lluosrif lleiaf cyffredin x+1 a x-1 yw \left(x-1\right)\left(x+1\right). Lluoswch \frac{5}{x+1} â \frac{x-1}{x-1}. Lluoswch \frac{6}{x-1} â \frac{x+1}{x+1}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}+\frac{6\left(x+1\right)}{\left(x-1\right)\left(x+1\right)})$$

Gan fod gan \frac{5\left(x-1\right)}{\left(x-1\right)\left(x+1\right)} a \frac{6\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} yr un dynodydd, adiwch nhw drwy adio eu rhifiaduron.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\left(x-1\right)+6\left(x+1\right)}{\left(x-1\right)\left(x+1\right)})$$

Gwnewch y gwaith lluosi yn 5\left(x-1\right)+6\left(x+1\right).

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x-5+6x+6}{\left(x-1\right)\left(x+1\right)})$$

Cyfuno termau tebyg yn 5x-5+6x+6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x+1}{\left(x-1\right)\left(x+1\right)})$$

Ystyriwch \left(x-1\right)\left(x+1\right). Gellir trawsnewid lluosi yn wahaniaeth rhwng sgwariau drwy ddefnyddio’r rheol: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x+1}{x^{2}-1^{2}})$$

Cyfrifo 1 i bŵer 2 a chael 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x+1}{x^{2}-1})$$

Ar gyfer unrhyw ddau ffwythiant y mae modd eu gwahaniaethu, deilliad cyniferydd dau ffwythiant yw’r enwadur wedi’i luosi â deilliad yr enwadur wedi’i dynnu o’r rhifiadur wedi’i luosi â deilliad yr enwadur, y cwbl wedi’i rannu â’r enwadur wedi'i sgwario.

$$\frac{\left(x^{2}-1\right)\frac{\mathrm{d}}{\mathrm{d}x}(11x^{1}+1)-\left(11x^{1}+1\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-1)}{\left(x^{2}-1\right)^{2}}$$

Deilliad polynomaial yw swm deilliadau ei dermau. Deilliad term cyson yw 0. Y deilliad o ax^{n} yw nax^{n-1}.

$$\frac{\left(x^{2}-1\right)\times 11x^{1-1}-\left(11x^{1}+1\right)\times 2x^{2-1}}{\left(x^{2}-1\right)^{2}}$$

Gwneud y symiau.

$$\frac{\left(x^{2}-1\right)\times 11x^{0}-\left(11x^{1}+1\right)\times 2x^{1}}{\left(x^{2}-1\right)^{2}}$$

Ehangu gan ddefnyddio’r briodwedd ddosbarthol.

$$\frac{x^{2}\times 11x^{0}-11x^{0}-\left(11x^{1}\times 2x^{1}+2x^{1}\right)}{\left(x^{2}-1\right)^{2}}$$

I luosi pwerau sy’n rhannu’r un sail, ychwanegwch eu hesbonyddion.

$$\frac{11x^{2}-11x^{0}-\left(11\times 2x^{1+1}+2x^{1}\right)}{\left(x^{2}-1\right)^{2}}$$

Gwneud y symiau.

$$\frac{11x^{2}-11x^{0}-\left(22x^{2}+2x^{1}\right)}{\left(x^{2}-1\right)^{2}}$$

Tynnu’r cromfachau diangen.

$$\frac{11x^{2}-11x^{0}-22x^{2}-2x^{1}}{\left(x^{2}-1\right)^{2}}$$

Cyfuno termau sydd yr un peth.

$$\frac{\left(11-22\right)x^{2}-11x^{0}-2x^{1}}{\left(x^{2}-1\right)^{2}}$$

Tynnu 22 o 11.

$$\frac{-11x^{2}-11x^{0}-2x^{1}}{\left(x^{2}-1\right)^{2}}$$

Ar gyfer unrhyw derm t, t^{1}=t.

$$\frac{-11x^{2}-11x^{0}-2x}{\left(x^{2}-1\right)^{2}}$$

Ar gyfer unrhyw derm t ac eithrio 0, t^{0}=1.

$$\frac{-11x^{2}-11-2x}{\left(x^{2}-1\right)^{2}}$$