Question

Simplify the expression

x2 − 5x + 6 / x − 3
to lowest terms, and identify the value(s) of x that must be excluded to avoid
division by zero.

Answer 1

`(x^3-7x^2+15x+6)/(x-3)`

Explanation:

`x^2-5x+(6)/(x-3)`

applying the minimum common multiple for each term

minimum common multiple: common and not common with its greatest exponent.

It is divided by the denominator and multiplied by the numerator

`((x^2.(x-3))-(5x.(x-3))+6)/(x-3)`

apply distributive property

`(x^3-3x^2-5x^2+15x+6)/(x-3)`

group similar terms

`(x^3-7x^2+15x+6)/(x-3)`