Question

How do you simplify `\frac { 5} { 4x ^ { 4} - 20x ^ { 3} } - \frac { 8} { 7x - 6}`?

Answer 1

`(-32x^4+160x^3+35x-30)/(4x^3(x-5)(7x-6)x^3`

Explanation:

Writing you first summand in the form

`(5(7x-6))/(4x^3(x-5)(7x-6))`
and the second

`(8*4*x^3*(x-5))/(4x^3(x-5)(7x-6))`
Now we can add both.

`(35x-30-32x^4+160x^3)/(4x^3(x-5)(7x-6))`

Answer 2

Cross Multiply,

Explanation:

`5/(4x^4-20x^3)-8/(7x-6)` is `(5(7x-6)-8(4x^4-20x^3))/((4x^4-20x^3)*(7x-6))`
which is `(35x-30-32x^4+160x^3)/(28x^5-28x^4-140x^4+120x^3)`
and simplifies to
`(35x-30-32x^4+160x^3)/(28x^5-168x^4+120x^3)`

There is no possible further factorization,