Question

How do you simplify this problem? (In comments)

Answer 1

\[(\sqrt{1-x ^{2}})(\frac{ 1 }{ \sqrt{1+y ^{2}} }) + (x)(\frac{ y }{ \sqrt{1+y ^{2}} })\]

Answer 2

the right answer is: \[\frac{ 1 }{ \sqrt{1+y ^{2}} } (\sqrt{1-x ^{2}} + xy)\] but I don't know what steps to take to get to this solution.

Answer 3

you need to cross multiply

Answer 4

no he doesn't

Answer 5

Abby are you here

Answer 6

i'm here now...sorry about that.

Answer 7

\[a\frac{ b }{ c }=\frac{ a \times b }{ c }\]
\[\sqrt{1-x^{2}}\frac{ 1 }{ \sqrt{1+y^{2}} } + x \frac{ y }{ \sqrt{1+y^{2}} }=\frac{ \sqrt{1-x^{2}} \times 1 }{ \sqrt{1+y^{2}} } + \frac{ x \times y }{ \sqrt{1+y^{2}} }\]

so anything multiplied by 1, is itself
x x y=xy

so you can tidy that up

now you need to know

\[\frac{ a }{ b } + \frac{ c }{ b }=\frac{ a +c }{ b }\]

\[\frac{ \sqrt{1-x^{2}} }{ \sqrt{1+y^{2}} } + \frac{ xy }{\sqrt{1+y^{2}} }=\frac{ \sqrt{1-x^{2}}+xy }{ \sqrt{1+y^{2}} }\]
Personally I would keep it like this, but your given answer is different,

so just take out a factor of 1

\[\frac{ \sqrt{1-x^{2}}+xy }{ \sqrt{1+y^{2}} }=\frac{ 1 }{ \sqrt{1+y^{2}} }(\sqrt{1-x^{2}}+xy)\]