Réitigh a/1+a+b/1+b

$$\frac { a } { 1 + a } + \frac { b } { 1 + b }$$

Luacháil

$$\frac{2ab+a+b}{\left(a+1\right)\left(b+1\right)}$$

Céimeanna gearra réitigh

Chun cothromóidí a shuimiú nó a dhealú, fairsingigh iad chun a n-ainmneoirí a mheaitseáil. Is é an t-iolrach is lú coitianta de 1+a agus 1+b ná \left(a+1\right)\left(b+1\right). Méadaigh \frac{a}{1+a} faoi \frac{b+1}{b+1}. Méadaigh \frac{b}{1+b} faoi \frac{a+1}{a+1}.

$$\frac{a\left(b+1\right)}{\left(a+1\right)\left(b+1\right)}+\frac{b\left(a+1\right)}{\left(a+1\right)\left(b+1\right)}$$

Tá an t-ainmneoir céanna ag \frac{a\left(b+1\right)}{\left(a+1\right)\left(b+1\right)} agus \frac{b\left(a+1\right)}{\left(a+1\right)\left(b+1\right)} agus, mar sin, is féidir iad a shuimiú trína n-uimhreoirí a shuimiú.

$$\frac{a\left(b+1\right)+b\left(a+1\right)}{\left(a+1\right)\left(b+1\right)}$$

Déan iolrúcháin in a\left(b+1\right)+b\left(a+1\right).

$$\frac{ab+a+ab+b}{\left(a+1\right)\left(b+1\right)}$$

Cumaisc téarmaí comhchosúla in: ab+a+ab+b.

$$\frac{2ab+a+b}{\left(a+1\right)\left(b+1\right)}$$

Fairsingigh \left(a+1\right)\left(b+1\right)

$$\frac{2ab+a+b}{ab+a+b+1}$$

Difreálaigh w.r.t. a

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