Complete the rational operation (3)/(x - 5) - (x)/(5)

Question

Complete the rational operation

`(3)/(x - 5) - (x)/(5)`

Answer 1

We have
3 / (x-5) - x/5
We make the GCF and we have
15/[ 5(x-5) ] - x(x-5)/[ 5(x-5)]
= [ 15 - x(x-5) ] [5(x-5)]
= [ 15 - x^2 + 5x] / [ 5 (x-5) ]
= [15 - x^2 + 5x]/[5x - 25]
An answer to your question is (15-x^2+5x)/(5x-25)