Question

please help me answer the question in the image

Answer 1

Answer:

2x/x+2

Step-by-step 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

Answer 2

Hey there!

Answer: $\Rightarrow \boxed {\sf{\frac{2x}{(x+2)}}}$

Solving steps:-

$\rightarrow\sf{\frac{ {2x}^{2} + 8x}{ {x}^{2} + 6x + 8} }$

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

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

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

$\rightarrow\sf{\frac{ 2x}{ (x + 2)} }$

~Done~