Indicate the domain of each fraction. a. (2y)/(9+y^(2) ) b. (5x)/(3x(x+12)) c. (7a)/((a+1)(a-4))

Question

Indicate the domain of each fraction.

a.
`(2y)/(9+y^(2) )`
b.
`(5x)/(3x(x+12))`
c.
`(7a)/((a+1)(a-4))`

Answer 1

Answer: see below

Explanation:

The denominator of the equations cannot equal zero.

a.
`9+y^(2)`
`= 0`

`y^(2) = -9`

`\sqrt{y^(2) } = √(-9)`

`y=-3i,3i`

The domain is all real numbers.

D:xE(−∞,∞)

b.3x(x+12)=0

3x=0, x+12=0

x=0,x=-12

D:xE(−∞.-12) U (-12,0) U (0,∞)

c.(a+1)(a-4)=0

a+1=0, a-4=0

a=1, a=4

D:xE(−∞.1) U (1,4) U (4,∞)