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sizzlingkavya

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The rational Equation
1/(x + 1) - 2/(x -1) = 3.
has two solutions. The smaller is _____________ and the larger is _________________.

after solving this I got the equation
3x^2 + x = 0
now how can I solve this equation. Please help!
 
sizzlingkavya said:
The rational Equation
1/(x + 1) - 2/(x -1) = 3.
has two solutions. The smaller is _____________ and the larger is _________________.

after solving this I got the equation
3x^2 + x = 0

x(3x + 1) = 0

Does that help?.....

now how can I solve this equation. Please help!
Click to expand...
 
sizzlingkavya said:
… how can I find the values [from the factored] equation?
Click to expand...


Subhotosh factored the lefthand side for you; there are two factors, and their product is zero.

(x) (3x + 1) = 0

You understand that each factor (x) and (3x + 1) represent some Real numbers, right? (The value of these two numbers change, as the value of x varies.)

There are only three ways to get zero when multiplying two Real numbers together.

1) The first number is zero and the second number is not
2) The second number is zero and the first number is not
3) Both numbers are zero

In other words, since the product (x)(3x + 1) equals zero, either (x) must be zero or (3x + 1) must be zero.

This is called the Zero-Product Property. It basically says that a product of factors will always equal zero, if any of the factors equal zero. Look it up in the index of a textbook or google, to find a formal definition and examples.

So, to find the values of x that make the product (x)(3x + 1) equal zero, we simply set each factor equal to zero to find a value for x that makes each factor zero.

x = 0

3x + 1 = 0

Obviously, zero is one solution for x.

Solve the other equation above to get the second solution.

 
BabyGirl2009 said:
I need help with a equaltion that is 9b+6=10b-8 what do i do to get what b is? :D :?:
Click to expand...
You do what your math teacher taught you.

By the way, you should start your own thread.
 
this is so simple, here is your equation,
9b+6=10b-8
now, 10b - 8 - 9b - 6 = 0
1b -14 = 0
b = 14
this is the answer
 
9b + 6 = 10b - 8

9b and 10b both have the same variable (the variable b), so they are like terms. To simplify the equation you need to put 10b on the left side of the equation.
To do this you subtract -10b from both sides of the equation because anything you do to one side of the equation you must do to the other side:
9b + 6 - 10b = 10b - 10b -8

10b minus 10b equals 0, so now the equation looks like: 9b + b - 10b = - 8

Because 9b and 10b are like terms you add them: 9b minus 10b equals -b
Now we have: -b + 6 = -8

6 and -8 are also like terms so now we will put 6 on the other side of the equation: -b + 6 - 6 = -8 - 6
then add -8 and -6: -b = -14 or b = 14

Hope that helped. :)
 
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