Factorise the following

Question

Solve the following: 14/x-3 - 5/x+2 + 9x-13/6+x-x^2

Answer 1

6+x-x^2 factorises: (3-x)(2+x), and this is the LCM for combining the fractions.

So we have (-14(2+x)-5(3-x)+9x-13)/((3-x)(2+x))=(-28-14x-15+5x+9x-13)/((3-x)(2+x))=

-56/((3-x)(2+x)) or 56/((x-3)(2+x)).