Question

Please help me answer the question in the image

Answer 1

Hey there!

Answer:
`\Rightarrow \boxed {\sf{(2x)/((x+2))}}`

Solving steps:-

`\rightarrow\sf{\frac{ {2x}^(2) + 8x}{ {x}^(2) + 6x + 8} }`

`\rightarrow\sf{\frac{ 2x(x + 4)}{ {x}^(2) + 4x +2x + 8} }`

`\rightarrow\sf{( 2x(x + 4))/( x (x + 4) +2(x + 4)) }`

`\rightarrow\sf{\frac{ 2x\sout{(x + 4)}}{ \sout{(x + 4)} (x + 2)} }`

`\rightarrow\sf{( 2x)/( (x + 2)) }`

~Done~

Answer 2

2x/x+2

Explanation:

Factor out 2x in the numerator

Then you get: 2x(x+4)

Factor the denominator

Two numbers that multiply to 8 and add to 6(2 and 4)

So you get: (x+2)(x+4)

Now you have: (2x(x+4))/(x+2)(x+4)

Simplify by cancelling the x+4

2x/x+2