Question

X² – 3x – 2 over (x-3)(x - 2)(x - 1)

express the following in partial fractions . ( with proper step pls ) ​

Answer 1

Answer:
`\bold{(x)/(x^2-3x+2)+(1)/(x^2-3x+2)}`

Explanation:

`(x^2-3x-2)/((x-3)(x-2)(x-1)) \qquad ;x\\eq{1, 2, 3}\\\\\\\\\text{Factor the numerator}\quad \longrightarrow \quad ((x-3)(x+1))/((x-3)(x-2)(x-1))\\\\\\\text{Cancel out (x-3)}\quad \longrightarrow \quad (x+1)/((x-2)(x-1))\\\\\\\text{To separate them, just place each term in the numerator}\\ \text{over the entire denominator.}\\\\(x)/((x-2)(x-1))+(1)/((x-2)(x-1))\\\\\\=\large\boxed{(x)/(x^2-3x+2)+(1)/(x^2-3x+2)}`