Question

Please help 30 points

Answer 1

Answer: =
`(a)/(4(a+2))`

Explanation:

Let's find common denominator of the the other side first

we have:

2a-4= 2(a-2)

2a²-8 = 2(a²-4) = 2(a-2)(a+2)

a²+2a = a(a+2)

common denominator is 2a(a-2)(a+2)

combine right side:

`(a^(2)(a+2)-a(a^(2)+4)-4(a-2) )/(2a(a-2)(a+2)`

combine like terms on top:

`(a^(3)+2a^(2)-a^(3)-4a-4a+8 )/(2a(a-2)(a+2)`

`(2a^(2)-8x+8 )/(2a(a-2)(a+2)`

lets put the whole problem together.

`(a-2)/(4(a^(2)+4a+4) )` /
`(2a^(2)-8x+8 )/(2a(a-2)(a+2)`

When dividing fractions, keep the first, change the sign, flip the 2nd fraction

`(a-2)/(4(a^(2)+4a+4) )` *
`(2a(a-2)(a+2)/(2(a^(2)-4x+4) )` simplify more and then reduce

`(a-2)/(4(a+2)(a+2) )` *
`(2a(a-2)(a+2)/(2(a-2)(a-2) )`

=
`(a)/(4(a+2))`