Question

Can someone please help me factor this

Answer 1

`\huge\boxed{\bf\:1}`

Explanation:

`\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } * \frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }`

Take
`\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 }` & factorise it at first.

`\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \\= (\left(x-3\right)\left(x-1\right))/(\left(x-4\right)\left(x-3\right))\\= (x-1)/(x-4)`

Now factorise the next set :
`\frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }`.

`\frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\\= (\left(x-4\right)\left(x+6\right))/(\left(x-1\right)\left(x+6\right))\\= (x-4)/(x-1)`

Now, multiply the two simplified results.

`\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } * \frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\\= (x-1)/(x-4)* (x-4)/(x-1) \\= (\left(x-1\right)\left(x-4\right))/(\left(x-4\right)\left(x-1\right)) \\= \boxed{\bf\: 1}`

`\rule{150pt}{2pt}`