Question

Simplify a^2-3a over a^3-8a^2+12a to lowest terms

Answer 1

Thus, the simplest form of
`(a^2-3a)/(a^3-8a^2+12a)` is
`(a(a-3))/(a(a-2)(a-6))`

Explanation:

Given two expression

`a^2-3a` and
`a^3-8a^2+12a`

We first solve each expression seperately,

Consider the first expression
`a^2-3a`

Taking a common from both the terms, we get
`a(a-3)`

Consider the second expression
`a^3-8a^2+12a`

First take a common from the expression, we get
`a(a^2-8a+12)`

The term in brackets is a quadratic equation , we can solve quadratic by middle term splitting method,

Consider
`a^2-8a+12`

-8a can be written as -6a-2a

`a^2-6a-2a+12`

`\Rightarrow a(a-6)-2(a-6)`

`\Rightarrow (a-2)(a-6)`

Thus, the given expression
`a^2-3a` over
`a^3-8a^2+12a` can be written as,

`(a^2-3a)/(a^3-8a^2+12a)`

Thus,
`(a^2-3a)/(a^3-8a^2+12a)=(a(a-3))/(a(a-2)(a-6))`

'a' gets cancel from both numerator and denominator ,

We get
`(a^2-3a)/(a^3-8a^2+12a)=((a-3))/((a-2)(a-6))`

Thus, the simplest form of
`(a^2-3a)/(a^3-8a^2+12a)` is
`(a(a-3))/(a(a-2)(a-6))`