Help with next Algebra problems?

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jos_iqmath2010

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Simplify the rational expression:

1. (x^2) / (x^2 -4) -(minus) (x+1) / (x+2)

2. (y/x) - (x/y) /all that divided by (1/y) - (1/x)


Solve the equation:

1. (2x) / (x+1) = (2x-1) / (x)

2. 2x(4-x)^-1/2(this -1/2 is an exponent of (4-x) all that minus - 3sqrt(4-x) = 0


Solve each inequality:

1. (x^2) < (2x+8)

2. x(x-1)(x+2) > 0

3. (2x-3) / (x+1) <= 1


These exercises are from an Algebra review of STEWARTCALCULUS. I will really appreciate your help. Thanks.
 
jos_iqmath2010 said:
2x-3/x+1 <= 1
Click to expand...
Is that 2x - 3/x + 1 or (2x-3) / (x+1)?

Please review your other expressions/equations and repost using proper bracketing...
 
jos_iqmath2010 said:
Simplify the rational expression:

1. (x^2) / (x^2 -4) -(minus) (x+1) / (x+2)

2. (y/x) - (x/y) /all that divided into (1/y) - (1/x) \(\displaystyle Are \ you \ sure \ that \ it \ is \ "divided \ into"\)
\(\displaystyle instead \ of \ "divided \ by?"\)

What you have typed is equivalent to \(\displaystyle \frac{\frac{1}{y} - \frac{1}{x}}{\frac{y}{x} - \frac{x}{y}}.\)


Solve the equation:

1. (2x) / (x+1) = (2x-1) / (x)

2. \(\displaystyle > > >\)2x(4-x)^(-1/2) \(\displaystyle < < <\) (this -1/2 is an exponent of (4-x) all that minus - 3sqrt(4-x) = 0

\(\displaystyle You \ would \ use \ parentheses \ (or \ other\ grouping \ symbols) \ around \ the \ exponent.\)


Solve each inequality:

1. (x^2) < (2x+8)

2. x(x-1)(x+2) > 0

3. (2x-3) / (x+1) <= 1


These exercises are from an Algebra review of STEWARTCALCULUS. I will really appreciate your help. Thanks.
Click to expand...
 
jos_iqmath2010 said:
Simplify the rational expression:

1. (x^2) / (x^2 -4) -(minus) (x+1) / (x+2)

We need a common denominator, before we can subtract ratios. Do you understand what the phrase "common denominator" means?



2. (y/x) - (x/y) /all that divided into (1/y) - (1/x)

You wrote "divided into", and that means 1/y - 1/x is on the top.

Is that what you intended to say?
Click to expand...

Please tell us how far you've gotten, on each of your exercises. Otherwise, we have no idea where you're stuck. If you can form specific questions, that's best. Also, it's better to create separate threads for each exercise because discussing so many exercises at once becomes confusing.

 
Sorry, it is DIVIDED BY; and yes I know common denominators, but how to apply them to reach the final answer of the problem, is what I can not find out.

Here are the answer of those excercises:

A.

1. (1) / (x-2)

2. -(x+y)

B.

1. (1)

2. 12/5

C.

1. (-2,4)

2. (-2,0) U (1, infinite)

3. (-1, 4]

I need the procedures of them.
 
jos_iqmath2010 said:
1. (x^2) / (x^2 -4) -(minus) (x+1) / (x+2) \(\displaystyle . \ . \ . \ . \ . **\)

Solve the equation:

2. 2x(4-x)^-1/2(this -1/2 is an exponent of (4-x) all that minus - 3sqrt(4-x) = 0 \(\displaystyle . \ . \ . \ . \ . **\)
Click to expand...


jos_iqmath2010 said:
Simplify the rational expression:


2. (y/x) - (x/y) /all that divided by (1/y) - (1/x)


I will really appreciate your help. Thanks.
Click to expand...

\(\displaystyle **\) Do not type "-(minus)" or "minus -" because each of them form a double negative.
Use either "minus" or "-" for the subtraction.

____________________________________________________________________________________


\(\displaystyle \frac{y/x - x/y}{1/y - 1/x}\)

The least common denominator of all of the four fractions is xy. Multiply each of the fractions

by xy, and is is suggested that you write that l.c.d. as \(\displaystyle \frac{xy}{1}\) so you know that the xy is multiplying
just each numerator.


\(\displaystyle {\frac{\frac{xy}{1}(\frac{y}{x}) - \frac{xy}{1}(\frac{x}{y})}{\frac{xy}{1}(\frac{1}{y}) - \frac{xy}{1}(\frac{1}{x})}\)


Cancel what you can in each of the four products and continue.
 
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