The simplest form of the given expressions will be \((5-x)\).
What is expression ?
Expressions is a finite combination of symbols that is well-formed according to rules that depend on the context.
We have,
\(f(x)=25-x^2\)
\(g(x)=x+5=5+x\)
So,
\((\frac{f}{g} )x=\frac{f(x)}{g(x)}\) \(.....(i)\)
Now,
Simplify \(f(x)=25-x^2\), Using \(a^2-b^2=(a-b)(a+b)\)
I.e.
\(f(x)=25-x^2 =(5+x)(5-x)\)
Now, substituting this in equation \((i)\) ;
\((\frac{f}{g} )x=\frac{f(x)}{g(x)}\)
i.e.
\(\frac{f(x)}{g(x)}=\frac{ (5+x)(5-x)}{5+x}\)
Simplify ;
\(\frac{f(x)}{g(x)}= (5-x)\)
So, the simplest form is \((5-x)\) .
Hence, we can say that the simplest form of the given expressions will be \((5-x)\) .
To know more about expressions click here
https://brainly.com/question/14083225
#SPJ3
