Question

What is the simplified form of x minus 3 over x squared plus x minus 12 ⋅ x plus 4 over x squared plus 8x plus 16 ? 1 over the quantity x minus 4 squared 1 over the quantity x plus 3 times the quantity x minus 4 1 over the quantity x plus 4 squared 1 over the quantity x minus 3 times the quantity x plus 4

Answer 1

i think this is the answer to the first part

Answer 2

1 over the quantity x plus 4 squared

Explanation:

Given expression,

`(x-3)/(x^2+x-12).(x+4)/(x^2+8x+16)`

By middle term splitting,

`(x-3)/(x^2+4x-3x-12).(x+4)/(x^2+4x+4x+16)`

`(x-3)/(x(x+4)-3(x+4)).(x+4)/(x(x+4)+4(x+4))`

`(x-3)/((x-3)(x+4)).(x+4)/((x+4)(x+4))}`

`=(1)/(x+4).(1)/(x+4)`

Multiply the fractions,

`=(1)/((x+4)^2)`

= 1 over the quantity x plus 4 squared