Respuesta :
Answer:
[tex]\frac{4x}{2x+y} +\frac{2y}{2x+y}=2[/tex]
Step-by-step explanation:
Given:
The expression to simplify is given as:
[tex]\frac{4x}{2x+y} +\frac{2y}{2x+y}[/tex]
Since, the denominator is same, we add the numerators and divide it by the same denominator. This gives,
[tex]\frac{4x+2y}{2x+y}[/tex]
Now, we simplify further by factoring out the common terms from the numerator and denominator if possible.
We observe that, 2 is a common factor to both [tex]4x\ and\ 2y[/tex]. So, we factor out 2 from the numerator. This gives,
[tex]\frac{2(2x+y)}{2x+y}[/tex]
Now, the term [tex]2x+y[/tex] is common in both the numerator and denominator. Hence, [tex]\frac{2x+y}{2x+y}=1[/tex]
So, the simplified form is:
[tex]=2\times \frac{2x+y}{2x+y}\\\\=2\times 1\\\\=2[/tex]
