Question

What is the sum? StartFraction 3 Over x squared minus 9 EndFraction StartFraction 5 Over x 3 EndFraction.

Answer 1

The sum of the two fractional number, which consist in the variable x is in the polynomial function,

$f(x)=\dfrac{5x-12}{(x+3)(x-3)}$

What is the sum of fraction number?

Fraction number is the number which is a part of a whole number. It is written with a numerator and denominator.

Fraction number are written as,

$\dfrac{a}{b}$

Here (a) is the numerator and (b) is the denominator.

To find the sum of two fraction numbers, cross multiply both the numbers or find the least common factor as denominator.

The first fraction number given in the problem is,

$\dfrac{3}{x^2+9}$

The second fraction number given in the problem is,

$\dfrac{5}{x+3}$

Let the sum of these number is f(x). Thus,

$f(x)=\dfrac{3}{x^2-9}+\dfrac{5}{x+3}\\f(x)=\dfrac{3}{(x+3)(x-3)}+\dfrac{5}{x+3}$

Solve it further as,

$f(x)=\dfrac{3+5(x-3)}{(x+3)(x-3)}\\f(x)=\dfrac{3+5x-15}{(x+3)(x-3)}\\f(x)=\dfrac{5x-12}{(x+3)(x-3)}$

Thus, the sum of the two fractional number is,

$f(x)=\dfrac{5x-12}{(x+3)(x-3)}$

Learn more about the fraction number here:

brainly.com/question/78672