I need help with my algebra homework quickly please thank you

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

1) Break the question up so that is it easier to comprehend. So first try to solve (5/x) + (1/3x). To solve this, you need a common denominator, which is 3x. Since (1/3x) already has 3x as its denominator, you simply have to multiply 3 to both the numerator and denominator of (5/x). When you do this, you will get (15/3x). With this new fraction, you can now easily add the two fractions together to get (16/3x).

Now you can focus on the bottom part of fraction which is (2/3x) + (1/2x). Doing what we did before, we must find a common denominator which is 6x. So we much multiply (2/2) with (2/3x) which is (4/6x). Then multiple (3/3) with (1/2x) which will result in (3/6x). With these new fractions, you can add (4/6x) and (3/6x) easily to get (7/6x). Now our new problem is simply (16/3x) / (7/6x). With this, we can use KCF (Keep, change, and flip) to change our problem to (16/3x) x (6x/7). You can then easily multiply the fractions as usual to receive an answer of (32/7) which is option D.

2) For this problem, you must try to simplify the fraction. x²-4 is a difference of two squares, therefore, you can break it up and make it (x-2)(x+2). Once you've done that, your new fraction is (x-2)(x+2) / (x+2). The (x+2) from the numerator and denominator cancel each other out, which leaves you with just (x-2), which is a linear expression and can be easily graphed as option C.