U must draw a diagarm to check the length first
Xbxkskeshxikrjdkwwkndjxjx
Answer:
x > - 2
x ∈ ( - 2 ; + oo)
Step-by-step explanation:
- 5x < 10 | *(-)
5x > - 10 | : 2
x > - 2
x ∈ ( - 2 ; + oo)
ANSWER
Vertical asymptote:
x=1
Horizontal asymptote:
y=1
EXPLANATION
The given rational function is
The vertical asymptote occurs at
The vertical asymptotes is x=1
The degree of the numerator is the same as the degree of the denominator.
The horizontal asymptote of such rational function is found by expressing the coefficient of the leading term in the numerator over that of the denominator.
y=1
We need to find two numbers that multiply to 24 (last coefficient) and add to 10 (middle coefficient). Through trial and error, the two values are 6 and 4
6 + 4 = 10
6*4 = 24
So we can break up the 10ab into 6ab+4ab and then use factor by grouping
a^2 + 10ab + 24b^2
a^2 + 6ab + 4ab + 24b^2
(a^2+6ab) + (4ab+24b^2)
a(a+6b) + 4b(a+6b)
(a+4b)(a+6b)
Therefore, the original expression factors completely to (a+4b)(a+6b)
