${5x+4\over -x^2-x+2}$
My solution:
${5x+4\over -x^2-x+2}$
$= {5x+4\over -(x-1)(x+2)}$
$= {A\over (x-1)} + {B\over (x+2)}$
$= {3\over -(x-1)} + {2\over -(x+2)}$
$= -{3\over x-1} -{2\over x+2}$
Can I multiply both fractions by -1 as follows:
Rather than writing:
$ -{3\over x-1} -{2\over x+2}$
I could multiply the first fraction denominator by -1
${3\over -1*(x-1)} = {3\over 1-x}$
ditto for the second fraction to get:
${2\over -1* (x+2)} = {2\over -x-2}$
Are my solutions correct ?
Yes, they are correct : $$\frac{5x+4}{-x^2-x+2}=\frac{3}{1-x}\color{red}{+}\frac{2}{-x-2}.$$