I am new and I need help with my algebra homework as soon as possible please

Question

1.) Simplify. Assume that all variables represent nonzero numbers.

A.) 

B.) None of these

C.) 

D.) 

E.) 

2.) Graph:

A.)

B.) 

C.)



D.)

Answer 1

Problem 1

First you want to write both the numerator and denominator portions in terms of a common denominator.

numerator: 5/x + 1/3x = 15/3x + 1/3x = 16/3x

denominator: 2/3x + 1/2x = 4/6x + 3/6x = 7/6x

Now the expression is (16/3x)/(7/6x). All we need to do is divide the fractions.

The answer should be D) 32/7

Problem 2

First notice that x²-4 can be factored as follows (x+2)(x-2). Now (x+2) in the numerator and denominator will cancel out. Simplifying f(x) = x -2. However, the original expression has an x + 2, in the denominator, which means that when x = -2, f(x) will be undefined. We make a note of this by drawing a hole in the line where x = -2.

Answer is C.