Question

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

Answer 1

Answer:

Thus, the simplest form of $\frac{a^2-3a}{a^3-8a^2+12a}$ is $\frac{a(a-3)}{a(a-2)(a-6)}$

Step-by-step 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,

$\frac{a^2-3a}{a^3-8a^2+12a}$

Thus, $\frac{a^2-3a}{a^3-8a^2+12a}=\frac{a(a-3)}{a(a-2)(a-6)}$

'a' gets cancel from both numerator and denominator ,

We get $\frac{a^2-3a}{a^3-8a^2+12a}=\frac{(a-3)}{(a-2)(a-6)}$

Thus, the simplest form of $\frac{a^2-3a}{a^3-8a^2+12a}$ is $\frac{a(a-3)}{a(a-2)(a-6)}$