SOLUTION: Write each fraction in terms of the LCM of the denominators. 2x/ x2 + x − 42 , −4x/ x2 + 13x + 42

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Write each fraction in terms of the LCM of the denominators. 2x/ x2 + x − 42 , −4x/ x2 + 13x + 42       Log On


   

Question 1205157: Write each fraction in terms of the LCM of the denominators.

2x/
x2 + x − 42
,
−4x/
x2 + 13x + 42
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Factor the denominators
x%5E2%2Bx-42+=+%28x%2B7%29%28x-6%29
x%5E2%2B13x%2B42+=+%28x%2B7%29%28x%2B6%29
The unique factors are: (x+7), (x-6), and (x+6)

The LCM is the product of those unique factors (x+7)(x-6)(x+6)
We could expand that out but I'll leave that for the student as an exercise.

The first fraction
%282x%29%2F%28x%5E2%2Bx-42%29
is the same as
%282x%29%2F%28%28x%2B7%29%28x-6%29%29
It is missing (x+6) to have its denominator reach the LCD.
Multiply top and bottom by (x+6) to get the denominator to the LCD.



The second fraction
%28-4x%29%2F%28x%5E2%2B13x%2B42%29
is the same as
%28-4x%29%2F%28%28x%2B7%29%28x%2B6%29%29
It is missing (x-6) to have its denominator reach the LCD.
Multiply top and bottom by (x-6) to get the denominator to the LCD.

I'll let the student expand out those expressions if your teacher requires it.