3/(x-4)=-3/(x+1)+9/(x-4)(x+1),6x/(x^2-1)-3/(x^2+x-2),|6t-2|<

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.

3/(x-4)=-3/(x+1)+9/(x-4)(x+1),6x/(x^2-1)-3/(x^2+x-2),|6t-2|<

Hi,

The following four problems have been killing me! I just can't figure them out ...

Puh leeeze I need help ... thx
needhelp

Posts: 1
Joined: Sat Jan 31, 2009 10:51 pm

No instructions were included, so I'll have to guess at what you're needing to do. Also, since no work was included, I'll provide links so you can learn the basics first.

$\mbox{1. Solve }\, \frac{3}{x\, -\, 4}\, =\, \frac{-3}{x\, +\, 1}\, +\, \frac{9}{(x\, -\, 4)(x\, +\, 1)}$

To solve this rational equation, a good first step will be to multiply through by the common denominator.

. . . . .Solving Rational Equations
. . . . .Multiplying Polynomials

Once you have studied the lessons, try to follow the instructions. After multiplying through, you should end up with:

. . . . .$3(x\, +\, 1)\, =\, -3(x\, -\, 4) + 9$

Multiply out, and solve the resulting linear equation for "x=". Remember to check for any division-by-zero problems with the original equation! (There won't be any, in this case, but it's a good idea to show your "check" anyway.)

$\mbox{2. Simplify }\, \frac{6x}{x^2\, -\, 1}\, -\, \frac{3}{x^2\, +\, x\, -\, 2}$

To simplify this rational expression (this polynomial fraction sum), you will need to convert to the common denominator. To find this denominator, you will first need to factor the denominators. Once you have converted the fractions to this common denominator, you can combine the numerators and simplify the result.

. . . . .Factoring Quadratics
. . . . .Special Factoring
. . . . .Adding Rational Expressions

You should arrive at a common denominator of:

. . . . .$(x\, -\, 1)(x\, +\, 1)(x\, +\, 2)$

After converting the fractions to this denominator, you should reach the following point:

. . . . .$\frac{6x(x\, +\,2)\, -\, 3(x\, +\, 1)}{(x\, -\, 1)(x\, +\, 1)(x\, +\, 2)}$

Multiply out the numerator, but not the denominator. Then complete the simplification. You'll be able to factor a "3" out of the numerator, but that's it.

$\mbox{3. Solve }\,\left|6t\,-\,2\right|\leq6$

To solve this absolute-value inequality, you'll need to know about absolute values, solving linear equations, and solving linear inequalities. Then put the different pieces together to solve this exercise.

. . . . .Absolute Values
. . . . .Solving Linear Equations
. . . . .Soving Linear Inequalities
. . . . .Solving Absolute-Value Equations
. . . . .Solving Absolute-Value Inequalities

Once you've studied the above, take the argument out of the absolute-value bars according to the rules for "less than" inequalities:

. . . . .$-6\, \leq\, 6t\, -\, 2\, \leq\, 6$

A good start will be to divide though, on all three "sides", by 2. Then add 1 to all three "sides", and divide by 3.

$\mbox{4. Solve }\,\left|1\,-\,9x\right|>3$

This one works just like Exercise (3), except that you'll start by splitting the inequality into two pieces:

. . . . .$1\, -\, 9x\, <\, -3\, \mbox{ or }\, 1\, -\, 9x\, >\, +3$

Then solve the two inequalities.

If you get stuck, please reply showing your work and reasoning, so we can see where you're having difficulty. Thank you!

Eliz.

stapel_eliz

Posts: 1757
Joined: Mon Dec 08, 2008 4:22 pm