# operations with functions

### operations with functions

Hi its a math problem. i cant remember the rules for adding , subtracting, multiplying and dividing fractions with roots . for example ,f(x) the square root of x+1 added to f (g) 2/the square root of x+1 . the answer was x+3 over the square root of x+1 but i dont know how they obtained this. the rules etc. thank you

p.s. i would like to know what topic to study concerning the rules of adding , multiplying , dividing root fractions. thank you
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### Re: operations with functions

The rules for working with functions are exactly the same as the rules for working with numbers because, for any function, f, f(x) is a number! Here, $$f(x)= \sqrt{x+ 1}$$ so, for example, $$f(3)= \sqrt{3+1}= \sqrt{4}= 2$$. Similarly, with $$g(x)= \frac{2}{\sqrt{x+ 1}}$$ so that $$g(3)= \frac{2}{\sqrt{3+ 1}}= \frac{2}{2}= 1$$ so that $$(f+ g)(3)= 2+ 1= 3$$.

More generally, $$(f+ g)(x)= \sqrt{x+ 1}+ \frac{2}{\sqrt{x+ 1}}$$. To add fractions, you need to have the same denominator. Here, there is only the denominator $$\sqrt{x+ 1}$$ so we need to multiply the first term by $$\frac{\sqrt{x+ 1}}{\sqrt{x+ 1}}$$: $$\sqrt{x+ 1}\frac{\sqrt{x+1}}{\sqrt{x+1}}= \frac{x+ 1}{\sqrt{x+1}}$$. Adding that to $$\frac{2}{\sqrt{x+ 1}}$$, $$\frac{x+1}{\sqrt{x+1}}+ \frac{2}{\sqrt{x+1}}= \frac{x+ 3}{\sqrt{x+ 1}}$$. That is exactly what you would do if you were adding, say, $$1+ \frac{2}{3}= \frac{5}{3}$$.
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