Which shows the expressions rewritten with a common denominator? x-5/x+3 and 4/x-3

x-5/x+3  = (x² - 2x  -15)/(x² - 9)  

4/x-3 = (4x + 12)/(x² - 9)

Step-by-step explanation:

Points to remember

(a + b)(a - b) = a² - b²

It is given two expression,

x-5/x+3 and 4/x-3

To find the common denominator

The first denominator is (x + 3) and the second denominator is (x - 3)

The common denominator is (x + 3)(x -3)

x-5/x+3 can be written as,

(x-5)/(x+3) * (x - 3)/(x - 3)

= (x² -5x + 3x -15)/(x² - 9)

= (x² - 2x  -15)/(x² - 9)

4/(x - 3) can be written as,

4/(x - 3) * (x + 3)(x + 3)

 = 4(x + 3)/(x - 3)(x + 3)

 = (4x + 12)/(x² - 9)

Therefore x-5/x+3 and 4/x-3 in common denominator is,

x-5/x+3  = (x² - 2x  -15)/(x² - 9)  

4/x-3 = (4x + 12)/(x² - 9)

the slope of the first function is -3. (3/1)

the slope of the second function is 1. (13-10/6-3).

since |-3| is greater than |1|, the function with the steepest slope is the first.