Question

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 − )

Answer 1

Answer:

$(x-4)$

Step-by-step explanation:

To complete the following steps, we just need to find the factor of each quadratic expression:

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

To find factors, we have to find two numbers, which product be 4, and difference be 3 (we say the difference, because both resulting factor have different signs). Those number are 4 and 1.

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

The first factor $(x-4)$ has a negative sign because it has to be the same sign of the second term of the quadratic expression, which is negative. The second factor $(x+1)$ has a positive sign because it's the product from the second term sign (-) and the third terms sing (+).

Then, we do the same process with $x^{2} -6x+8$:

$x^{2} -6x+8=(x-4)(x-2)$

Now, we replace each pair of factor for its quadratic expression as follows:

$x^{2} -3x-4=x^{2} -6x+8\\(x-4)(x+1)=(x-4)(x-2)$

You can see that the Least Common Denominator is $(x-4)$, actually it's the only common factor.

Answer 2

Answer:

x^2-3x-4=(x4)(x+1)

x^2-6x+8=(x-4)(x-2)

(x-4)(x+1)(x-2)

Step-by-step explanation: