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 − )

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:

Expand

Factorize

Factor out 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:

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Step-by-step explanation:

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

Factor of :

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,

The first factor 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 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 :

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

You can see that the Least Common Denominator is , actually it's the only common factor.