subtract the following rational expressions  \frac{8k}{9k - 4} - \frac{3k^3}{2k + 7} please show all work​

Question

subtract the following rational expressions
  \frac{8k}{9k - 4}  -  \frac{3k^3}{2k + 7}
please show all work​

in progress 0
Thiên Thanh 3 months 2021-07-24T15:27:22+00:00 2 Answers 2 views 0

Answers ( )

    0
    2021-07-24T15:28:30+00:00

     \frac{8k}{9k - 4} - \frac{3k^3}{2k + 7} \\  \\ \frac{8k(2k + 7)}{(9k - 4)(2k + 7)} - \frac{3k^3(9k - 4)}{(2k + 7)(9k - 4)} \\  \\ \frac{16k {}^{2}  + 56k}{(9k - 4)(2k + 7)} - \frac{27k {}^{4}  - 12k {}^{3} }{(2k + 7)(9k - 4)} \\  \\  \frac{16k {}^{2}  + 56k - 27k {}^{4}  +  12k {}^{3} }{(9k - 4)(2k + 7)}

    Terms can be re-arranged*.

    0
    2021-07-24T15:28:40+00:00

    Answer:

    -27k^4 +12k^3+16k^2+56k

    ———————

    (9k-4)(2k+7)      

    Step-by-step explanation:

    8k                  3k^3

    ———   –  ———–

    9k-4             2k+7

    Get a common denominator

    8k *(2k+7)          3k^3 *(9k-4)

    ———      –           ———–

    (9k-4)(2k+7)        (9k-4)(2k+7)

    Combine

    8k *(2k+7) -3k^3 *(9k-4)

    ———————

    (9k-4)(2k+7)        

    Distribute

    16k^2+56k -27k^4 +12k^3

    ———————

    (9k-4)(2k+7)      

    -27k^4 +12k^3+16k^2+56k

    ———————

    (9k-4)(2k+7)        

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )