Complete the following steps to find the LCD and write the sum of the numerators for the given problem: Factor each denominator:

Question

zimovet

20 days ago

13

Complete the following steps to find the LCD and write the sum of the numerators for the given problem: Factor each denominator:

x2 – 3x – 4 = x2 – 6x + 8 = The least common denominator is: (x − 4)(x + )(x − )

Mathematics

2 answers:

Zina [12.3K] · Answer 1 · 2026-04-01T18:33:14+03:00

Clarification:

To accomplish the next steps, we simply need to determine the factors of each quadratic expression:

Factors of $x^{2} -3x-4$ :

To identify factors, we must find two numbers whose product equals 4, with a difference of 3 (the difference is crucial since both resulting factors carry opposing signs). Those numbers are 4 and 1.

So, $x^{2} -3x-4=(x-4)(x+1)$

The initial factor $(x-4)$ is negative reflecting the sign of the quadratic expression's second term which is negative. The subsequent factor $(x+1)$ is positive due to the product from the second term sign (-) and the third term sign (+).

Next, we repeat this process with $x^{2} -6x+8$ :