Question

What is the sum? startfraction 3 over x squared minus 9 endfraction startfraction 5 over x 3 endfraction startfraction 8 over x squared x minus 6 endfraction startfraction 5 x minus 12 over x minus 3 endfraction startfraction negative 5 x over (x 3) (x minus 3) endfraction startfraction 5 x minus 12 over (x 3) (x minus 3)

Answer 1

The addition of the expression 5/(x² – 9) and 3/(x + 3) is (5x – 12)/[(x + 3)(x – 3)]. Then the correct option is D.

What is a fraction number?

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.

The expressions are given below.

$\rm \dfrac{3}{x^2 - 9} \ and \ \dfrac{5}{x+3}$

The sum of the expressions will be

$\rm \dfrac{3}{x^2 - 9} + \dfrac{5}{x+3}$

We know that the formula

a² – b² = (a + b)(a – b)

Then we have

$\rm \dfrac{3}{x^2 - 3^2} + \dfrac{5}{x+3}\\\\\\\rm \dfrac{3}{(x-3)(x+3)} + \dfrac{5}{x+3}\\\\\\\rm \dfrac{3+5(x-3)}{(x-3)(x+3)} \\\\\\\dfrac{3+5x-15}{(x-3)(x+3)} \\\\\\\dfrac{5x-12}{(x-3)(x+3)}$

The addition of the expression 5/(x² – 9) and 3/(x + 3) is (5x – 12)/[(x + 3)(x – 3)]. Then the correct option is D.

More about the fraction number link is given below.

https://brainly.com/question/78672