Least common denominator

Question

How do I find the LCD of k²+k-42/1-k and k²-k-30/k-1

Answer 1

To find the LCD you only have to focus on the denominators of each fraction: 1-k and k-1

Multiply them to each other by using the FOIL method: (1-k) * (k-1) = k-1-k²+k

Simplify the answer: k²+2k-1

Answer 2

k²  +  k  -  42                                                           k²  -  k  -  30

1        1    1-k                                                          1       1     k-1

The denominators are:

1  and  1-k                                                                 1 and k-1

This means you need to get the denominator to be:

1-k                                                                               k-1

In case you need help once you have the denominators. I will leave the original outside of parenthesis and the mulitplier inside. Remember you have to multiply both the top and bottom of a fraction if you are altering it in any way.

k² (1-k) +  k (1-k) -  42                                               k_²  (k-1) -  k (k-1) -  30

1  (1-k)     1 (1-k)    1-k                                               1  (k-1)    1  (k-1)   k-1

This gives you:

k² - k³ + k - k² - 42                                                    k³ - k² - k² - k - 30

           1-k                                                                           k-1

Simplify further and put into correct order:

-k³ + k - 42                                                                  k³ -2k² - k - 30

      1-k                                                                                 k-1