Datrys 4/2r+5+3/5r-2

$$\frac { 4 } { 2 r + 5 } + \frac { 3 } { 5 r - 2 }$$

Enrhifo

$$\frac{26r+7}{\left(5r-2\right)\left(2r+5\right)}$$

Camau Ateb Byr

I ychwanegu neu dynnu mynegiannau, rhaid i chi eu ehangu i wneud eu enwaduron yr un fath. Lluosrif lleiaf cyffredin 2r+5 a 5r-2 yw \left(5r-2\right)\left(2r+5\right). Lluoswch \frac{4}{2r+5} â \frac{5r-2}{5r-2}. Lluoswch \frac{3}{5r-2} â \frac{2r+5}{2r+5}.

$$\frac{4\left(5r-2\right)}{\left(5r-2\right)\left(2r+5\right)}+\frac{3\left(2r+5\right)}{\left(5r-2\right)\left(2r+5\right)}$$

Gan fod gan \frac{4\left(5r-2\right)}{\left(5r-2\right)\left(2r+5\right)} a \frac{3\left(2r+5\right)}{\left(5r-2\right)\left(2r+5\right)} yr un dynodydd, adiwch nhw drwy adio eu rhifiaduron.

$$\frac{4\left(5r-2\right)+3\left(2r+5\right)}{\left(5r-2\right)\left(2r+5\right)}$$

Gwnewch y gwaith lluosi yn 4\left(5r-2\right)+3\left(2r+5\right).

$$\frac{20r-8+6r+15}{\left(5r-2\right)\left(2r+5\right)}$$

Cyfuno termau tebyg yn 20r-8+6r+15.

$$\frac{26r+7}{\left(5r-2\right)\left(2r+5\right)}$$

Ehangu \left(5r-2\right)\left(2r+5\right).

$$\frac{26r+7}{10r^{2}+21r-10}$$

Gwahaniaethu w.r.t. r

$$-\frac{260r^{2}+140r+407}{\left(\left(5r-2\right)\left(2r+5\right)\right)^{2}}$$

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 2r+5 a 5r-2 yw \left(5r-2\right)\left(2r+5\right). Lluoswch \frac{4}{2r+5} â \frac{5r-2}{5r-2}. Lluoswch \frac{3}{5r-2} â \frac{2r+5}{2r+5}.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{4\left(5r-2\right)}{\left(5r-2\right)\left(2r+5\right)}+\frac{3\left(2r+5\right)}{\left(5r-2\right)\left(2r+5\right)})$$

Gan fod gan \frac{4\left(5r-2\right)}{\left(5r-2\right)\left(2r+5\right)} a \frac{3\left(2r+5\right)}{\left(5r-2\right)\left(2r+5\right)} yr un dynodydd, adiwch nhw drwy adio eu rhifiaduron.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{4\left(5r-2\right)+3\left(2r+5\right)}{\left(5r-2\right)\left(2r+5\right)})$$

Gwnewch y gwaith lluosi yn 4\left(5r-2\right)+3\left(2r+5\right).

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{20r-8+6r+15}{\left(5r-2\right)\left(2r+5\right)})$$

Cyfuno termau tebyg yn 20r-8+6r+15.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{26r+7}{\left(5r-2\right)\left(2r+5\right)})$$

Cyfrifwch y briodoledd ddosrannol drwy luosi pob 5r-2 gan bob 2r+5.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{26r+7}{10r^{2}+25r-4r-10})$$

Cyfuno 25r a -4r i gael 21r.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{26r+7}{10r^{2}+21r-10})$$

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.

$$\frac{\left(10r^{2}+21r^{1}-10\right)\frac{\mathrm{d}}{\mathrm{d}r}(26r^{1}+7)-\left(26r^{1}+7\right)\frac{\mathrm{d}}{\mathrm{d}r}(10r^{2}+21r^{1}-10)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

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

$$\frac{\left(10r^{2}+21r^{1}-10\right)\times 26r^{1-1}-\left(26r^{1}+7\right)\left(2\times 10r^{2-1}+21r^{1-1}\right)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

Symleiddio.

$$\frac{\left(10r^{2}+21r^{1}-10\right)\times 26r^{0}-\left(26r^{1}+7\right)\left(20r^{1}+21r^{0}\right)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

Lluoswch 10r^{2}+21r^{1}-10 â 26r^{0}.

$$\frac{10r^{2}\times 26r^{0}+21r^{1}\times 26r^{0}-10\times 26r^{0}-\left(26r^{1}+7\right)\left(20r^{1}+21r^{0}\right)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

Lluoswch 26r^{1}+7 â 20r^{1}+21r^{0}.

$$\frac{10r^{2}\times 26r^{0}+21r^{1}\times 26r^{0}-10\times 26r^{0}-\left(26r^{1}\times 20r^{1}+26r^{1}\times 21r^{0}+7\times 20r^{1}+7\times 21r^{0}\right)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

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

$$\frac{10\times 26r^{2}+21\times 26r^{1}-10\times 26r^{0}-\left(26\times 20r^{1+1}+26\times 21r^{1}+7\times 20r^{1}+7\times 21r^{0}\right)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

Symleiddio.

$$\frac{260r^{2}+546r^{1}-260r^{0}-\left(520r^{2}+546r^{1}+140r^{1}+147r^{0}\right)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

Cyfuno termau sydd yr un peth.

$$\frac{-260r^{2}-140r^{1}-407r^{0}}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

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

$$\frac{-260r^{2}-140r-407r^{0}}{\left(10r^{2}+21r-10\right)^{2}}$$

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

$$\frac{-260r^{2}-140r-407}{\left(10r^{2}+21r-10\right)^{2}}$$