If f(x)=25-x^2 and g(x)=x+5, what is (f/g)(x)? Write your answer in the simplest form.

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fokasha fokasha · Answer 1 · 2016-11-06T19:58:45+01:00

f(x) = 25-x^2
g(x) =x+5

(25-x^2)/(x+5)
Factor the 25-x^2
(-x+5)(x+5)/(x+5)
The (x+5)s are common therefore cross out leaving you with (f/g)(x)= -x+5

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PallaviB PallaviB · Answer 2 · 2022-07-01T14:37:26+02:00

The simplest form of the given expressions will be [tex](5-x)[/tex].

Expressions is a finite combination of symbols that is well-formed according to rules that depend on the context.

We have,

[tex]f(x)=25-x^2[/tex]

[tex]g(x)=x+5=5+x[/tex]

So,

[tex](\frac{f}{g} )x=\frac{f(x)}{g(x)}[/tex] [tex].....(i)[/tex]

Now,

Simplify [tex]f(x)=25-x^2[/tex], Using [tex]a^2-b^2=(a-b)(a+b)[/tex]

I.e.

[tex]f(x)=25-x^2 =(5+x)(5-x)[/tex]

Now, substituting this in equation [tex](i)[/tex] ;

[tex](\frac{f}{g} )x=\frac{f(x)}{g(x)}[/tex]

i.e.

[tex]\frac{f(x)}{g(x)}=\frac{ (5+x)(5-x)}{5+x}[/tex]

Simplify ;

[tex]\frac{f(x)}{g(x)}= (5-x)[/tex]

So, the simplest form is [tex](5-x)[/tex] .

Hence, we can say that the simplest form of the given expressions will be [tex](5-x)[/tex] .

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