how can i solve this algebra

[gloomy ermine]

i need to calculate

(x+y+2)/(1+x)(1+y)

[obtuse plank]

lets write these 3 independently

$x^{2020}=\sqrt{11}-\sqrt{10}$

[mild lagoon]

yoavmal

[obtuse plank]

$y^{2020}=\sqrt{11}-\sqrt{10}$

[mild lagoon]

yoavmal

[obtuse plank]

and you need to calculate $\frac{x+y+2}{(1+x)(1+y)}$

yes?

[mild lagoon]

yoavmal

[obtuse plank]

@gloomy ermine

[gloomy ermine]

yes true

[gloomy ermine]

• instead of +

so

,tex $\frac{\left(\sqrt[2022]{\sqrt{11}+\sqrt{10}}+\sqrt[2022]{\sqrt{11}-\sqrt{10}}+2\right)}{\left(1+\sqrt[2022]{\sqrt{11}-\sqrt{10}}\right)\left(1+\sqrt[2022]{\sqrt{11}+\sqrt{10}}\right)}$

[mild lagoon]

LeKaizo

[gloomy ermine]

@obtuse plank

i need to calculate $\frac{\left(\sqrt[2022]{\sqrt{11}+\sqrt{10}}+\sqrt[2022]{\sqrt{11}-\sqrt{10}}+2\right)}{\left(1+\sqrt[2022]{\sqrt{11}-\sqrt{10}}\right)\left(1+\sqrt[2022]{\sqrt{11}+\sqrt{10}}\right)}$

[mild lagoon]

LeKaizo

[obtuse plank]

to me

this looks a lot like

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

[mild lagoon]

yoavmal

[gloomy ermine]

$\left(xy\right)^{2022}=11-1$

[mild lagoon]

LeKaizo

[gloomy ermine]

$xy=1$

[mild lagoon]

LeKaizo

[gloomy ermine]

$\frac{\left(x+y+2\right)}{1+y+2+xy}$

[mild lagoon]

LeKaizo

[gloomy ermine]

$\frac{\left(x+y+2\right)}{\left(x+y+2\right)}$

[mild lagoon]

LeKaizo

[gloomy ermine]

=1

[gloomy ermine]

also if i calculate this on the calculator i'll find 1

@obtuse plank

solved

[obtuse plank]

gg