Question

You don’t have to show the work but please help

Answer 1

`$((x+4)^(2))/(x-4) / (x^(2)-16)/(4 x-16)=(4(x+4))/((x-4))`

Solution:

Given expression is

`$((x+4)^(2))/(x-4) / (x^(2)-16)/(4 x-16)`

To solve this expression:

`$((x+4)^(2))/(x-4) / (x^(2)-16)/(4 x-16)=((x+4)^(2))/(x-4) / (x^(2)-4^2)/(4( x-4))`

Using algebraic identity:
`a^2-b^2=(a-b)(a+b)`

`$=((x+4)^(2))/(x-4) / ((x-4)(x+4))/(4( x-4))`

We can't solve it with division symbol. So change this into multiplication and solve it.

The second term is reversed when you change division into multiplication.

`$=((x+4)^(2))/(x-4) * (4(x-4))/(( x-4)(x+4))`

`$=((x+4)(x+4))/(x-4) * (4(x-4))/(( x-4)(x+4))`

`$=(4(x+4)(x+4)(x-4))/((x-4)( x-4)(x+4))`

Now, cancel the common terms in the numerator and denominator.

`$=(4(x+4))/((x-4))`

`$((x+4)^(2))/(x-4) / (x^(2)-16)/(4 x-16)=(4(x+4))/((x-4))`

Hence the answer is
`(4(x+4))/((x-4))`.