Answer:
First Picture Answer:
x=0, x=2/3 are extraneous Solutions
Second Picture Answer:
(-infinity, -3)(-3, infinity)
Third Picture Answer:
x=3
Fourth Picture Answer:
x=0, x=2 is extraneous solution
Fifth Picture Answer:
x=3/2 is the vertical asymptote
Step-by-step explanation:
First Picture Answer:
x/4=x^2/x+2
Multiply each side with 4(x+2)
x(x+2)=4x^2
x^2+2x-4x^2=0
-3x^2+2x=0
Taking x Common
x(-3x+2)=0
x=0, -3x+2=0
x=0, x=2/3
Second Picture Answer:
f(x)=x-1/x+3
A rational function is simply a fraction and in a fraction the denominator cannot be equal zero because it would be undefined. To find which numbers make the fraction undefined, create an equation where the denominator is not equal to zero.
x+3 is not equal to 0
x is not equal to -3
so our domain is (-infinity, -3)(-3, infinity)
Third Picture Answer:
3x-5/7=4/7
Multiply with 7 on both sides
3x-5=4
3x-=9
x=9/3
x=3
Fourth Picture Answer:
4x^2=(3x^2+2)x
4x^2=3x^2+2x
4x^2-3x^2-2x=0
x^2-2x=0
x(x-2)=0
x=0, x-2=0
x=0, x=2
Fifth Picture Answer:
Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of a rational function. Set the denominator of the above fraction equal to zero and solve, this will tell the values that x can not be:
2x-3=0
x=3/2
so x cannot be 3/2 which is the vertical asymptote
