please help me with this math?

Question

Solve the Equation.

1.2/5-3/x=1/5x
2.3/x+1-1/x=1/2
Sketch a graph of the Fuction.
3.y=1/x-3
4.y=1/x+1+1

Answer 1

First of all, you have GOT to put some parentheses in, so we know what the question is. I'm going to guess at what you mean for these, so they could be wrong.

1.2/5-3/x=1/5x
(2/5) - (3/x) = 1/(5x)

Common denominator is 5x...
(2x/5x) - (15 / 5x) = 1 / (5x)
(2x - 15) / 5x = 1 / 5x
5x(2x - 15) = 5x
10x^2 - 75x = 5x
10x^2 - 80x = 0
10(x^2 - 8x) = 0
x^2 - 8x = 0
x(x - 8) = 0
x = 0 and 8

2.3/x+1-1/x=1/2
[3 / (x + 1)] - (1 / x) = 1/2

CD is x(x + 1)

[(3)(x) - (x+1)] / x(x+1) = 1/2
(3x - x - 1) / (x^2 + x) = 1/2
(2x - 1) / (x^2 + x) = 1/2
2(2x - 1) = x^2 + x
2x - 2 = x^2 + x
0 = x^2 - x + 2

Using quadratic formula:
x = [-b +- sqrt (b^2 - 4ac)] / 2a
= [1 +- sqrt (-1^2 - 4(1)(2)] / 2(1)
= [1 +- sqrt (1 - 8)] / 2
= [1 +- sqrt (-7)] / 2
= [1 +- i sqrt 7] / 2

3 & 4)
we can't sketch graphs on this forum, so you're on your own there.

Answer 2

Well for the first one, you need a common denominator. So, use '5x' and multiply each term by that. You will find that some cancels and you have 2x - 15 = 1. Then, add 15 to both sides, to get that 2x = 16 or x = 8.

The second one, similar but a little longer. Took me a while here. Same concept, you need a common denominator. Problem is each term you must acknowledge separately here. In other words, multiply each by 2*x*(x+1). What you are left with is 6x-2x+2 = x squared + x. Do not panic with the x squared. I assume you have studied quadratics. Well, bring everything over to the right hand side. First you subtract the two x terms on the left giving you 2 = x squared - 3x. Then, subtract 2 leaving you with a quadratic equation of x squared - 3x - 2 = 0. Find the factors (x - 2)(x-1) giving you two answers of x = 2 or x = 1 (both work)

These last two will give you hyperbolas, I am at work and do not have my graphing calculator with me. But that is what they give you.

Answer 3

1). Bring the variables over to one side:
2/5 = 1/5x + 3/x (3x Becomes Positive due to crossing the
(=
2/5 = 1/5x + 15/5x (Common Denominator)
2/5 = 16/5x (Now Cross Multiply)
10x = 80 or x = 8

2. 3/x + 1 - 1/x = 1/2
2/x + 1 = 1/2
2/x = -1/2
2 = -1/2x
x = -4

3). Don't know how to graph on here to display this, Sorry