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

The least common denominator is simply the least expression that can be a common denominator for a set of rational expression

The least common denominator is (x - 4)(x + 1)(x - 2)

The equation is given as:

$\mathbf{x^2 -3x - 4 = x^2 - 6x + 8}$

Expand

$\mathbf{x^2 -4x + x - 4 = x^2 - 4x - 2x + 8}$

Factorize

$\mathbf{x(x -4) + 1(x - 4) = x(x - 4) - 2(x - 4)}$

Factor out x - 4

$\mathbf{(x +1)(x - 4) = (x - 2)(x - 4)}$

Both sides of the equation have a common factor i.e. x - 4

Hence, the least common denominator is (x - 4)(x + 1)(x - 2)

Read more about the least common denominator at:

https://brainly.com/question/12127721