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

You don’t have to show the work but please help-example-1

1 Answer

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$((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)).

User Maurice Perry
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